{"id":4351,"date":"2020-03-21T18:08:24","date_gmt":"2020-03-21T09:08:24","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?p=4351"},"modified":"2020-03-23T18:43:05","modified_gmt":"2020-03-23T09:43:05","slug":"sasa-textbook-math1-04","status":"publish","type":"post","link":"https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/","title":{"rendered":"[\uc218\ud559\u2160] \uc81c3\uc7a5 \ubb38\uc790\uc640 \uc2dd(1)"},"content":{"rendered":"<p><!-- \n\n\n<h2 style=\"text-align: center; margin-top: 1em; margin-bottom: 0.5em;\"> \uc81c1\uc7a5 \uc7a5\uc81c\ubaa9 <\/h2>\n\n\n\n\n<h2> 1.1 \uc808\uc81c\ubaa9 <\/h2>\n\n\n\n\n<h3> \uc18c\uc808\uc81c\ubaa9 <\/h3>\n\n\n <span class=\"defined\"> \ubcfc\ub4dc<\/span>\n\n\n\n<p> <span class=\"definition\"> \ubcf4\uae30 <\/span>\n\ubcf4\uae30 \ub0b4\uc6a9\n\n\n<ol class=\"parenthesis\"> \n\t\n\n<li> \uad04\ud638 \ubc88\ud638 \ubaa9\ub85d <\/li>\n\n\n<\/ol>\n\n\n<\/p>\n\n\n\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-301.png\" alt=\"\" width=\"150\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/>\n[efn_note]\ud517\ub178\ud2b8[\/efn_note]\n\n\n\n<div class=\"definition\">\n\t\n\n<p>\n\t\t<span class=\"definition\"> Definition 1.1.1 <\/span>\n\uc815\uc758 \ub0b4\uc6a9\n<\/p>\n\n<\/div>\n\n\n\n\n\n<blockquote>\n\uc778\uc6a9\ubb38\n<\/blockquote>\n\n\n\n\n\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 1.1<\/span>\n\uc608\uc81c \ub0b4\uc6a9 \ud639\uc740 \uc720\uc81c\n<\/p>\n\n\n\n\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span>\n\ud480\uc774 \ub610\ub294 \uc99d\uba85\n<span class=\"qed\"><\/span>\n<\/p>\n\n\n\n\n\n\n<div class=\"theorem\">\n\t\n\n<p>\n\t\t<span class=\"theorem\"> Theorem 1.1.3 <\/span>\n\uc815\ub9ac \ub0b4\uc6a9\n<\/p>\n\n\n<\/div>\n\n\n--><\/p>\n<style type=\"text\/css\">\nspan.hfill {\nfloat: right; \n}\n<\/style>\n<h2 style=\"text-align: center; margin-top: 1em; margin-bottom: 0.5em;\"> \uc81c3\uc7a5 \ubb38\uc790\uc640 \uc2dd <\/h2>\n<h2> 3.1 \ub2e4\ud56d\uc2dd <\/h2>\n<h3> \ub2e4\ud56d\uc2dd\uc758 \uad6c\uc870<span id='easy-footnote-1-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-1-4351' title='\ub2e4\ud56d\uc2dd\uc740 \uc5ec\ub7ec\ubaa8\ub85c \uc815\uc218\uc640 \uc720\uc0ac\ud55c \uad6c\uc870\ub97c \uac16\uace0 \uc788\ub2e4.'><sup>1<\/sup><\/a><\/span> <\/h3>\n<p>\ubb38\uc790 \ub610\ub294 \uc218\ub4e4\uc758 \uacf1\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc2dd\uc744 \ud56d\uc774\ub77c \ud558\uace0, \ud56d \ub610\ub294 \ud56d\ub4e4\uc758 \ud569\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc2dd\uc744 <span class=\"defined\">\ub2e4\ud56d\uc2dd<\/span>(polynomial)\uc774\ub77c\uace0 \ud55c\ub2e4.<span id='easy-footnote-2-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-2-4351' title='\ud558\ub098\uc758 \ud56d\uc73c\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c4 \ub2e4\ud56d\uc2dd\uc740 &lt;span class=&quot;defined&quot;&gt;\ub2e8\ud56d\uc2dd&lt;\/span&gt;(monomial)\uc774\ub77c \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4.'><sup>2<\/sup><\/a><\/span>  \uc608\ub97c \ub4e4\uc5b4<br \/>\n\\[<br \/>\n\\pi,\\quad x,\\quad 3z+1,\\quad -x+2x^{2020}+2, \\quad -xy^{2}+x^{2}+a^{4}y^{2}+x<br \/>\n\\]<br \/>\n\ub294 \ubaa8\ub450 \ub2e4\ud56d\uc2dd\uc774\ub2e4.<span id='easy-footnote-3-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-3-4351' title='\\(x\\)\uc5d0 \ub300\ud55c \ub2e4\ud56d\uc2dd, \\(x, y\\)\uc5d0 \ub300\ud55c \ub2e4\ud56d\uc2dd \ub4f1\uacfc \uac19\uc774 \ub9d0\ud558\ub294 \uac83\ub3c4 \uc88b\ub2e4.'><sup>3<\/sup><\/a><\/span> <span id='easy-footnote-4-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-4-4351' title='\uc0c1\uc218 \ub2e4\ud56d\uc2dd\uc774 \uc544\ub2cc \ub2e4\ud56d\uc2dd\uc774 \uc788\uc744 \ub54c, \uadf8 \ub2e4\ud56d\uc2dd\uc758 \ud56d\ub4e4\uc774 \uac16\ub294 \ucc28\uc218 \uc911\uc5d0\uc11c \uac00\uc7a5 \ud070 \uac83\uc744 \uadf8 \ub2e4\ud56d\uc2dd\uc758 \ucc28\uc218\ub77c \ud55c\ub2e4. \\(-xy^{2}+x^{2}+a^{4}y^{2}+x\\)\uc758 \ucc28\uc218\ub294 \ubb34\uc5c7\uc77c\uae4c?'><sup>4<\/sup><\/a><\/span><\/p>\n<p>\n\ub2e4\ud56d\uc2dd\uc740 \ub3d9\ub958\ud56d\ub07c\ub9ac \ubaa8\uc544\uc11c \uc815\ub9ac\ud558\uc5ec \uac04\ub2e8\ud788 \ub098\ud0c0\ub0b8\ub2e4. \uadf8\ub9ac\uace0  \ucc28\uc218\uac00 \ub192\uc740 \ud56d\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ub098\uc5f4\ud558\ub294 \ub0b4\ub9bc\ucc28\uc21c \ud639\uc740 \ucc28\uc218\uac00 \ub0ae\uc740 \ud56d\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ub098\uc5f4\ud558\ub294 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uba74 \ubcf4\uae30 \uc88b\ub2e4.<span id='easy-footnote-5-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-5-4351' title='\uc660\uc9c0 \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\ub294 \uac83\uc774 \ub9c8\uc74c\uc774 \ud3b8\ud55c \uac83 \uac19\uae34\ud55c\ub370&amp;#8230;'><sup>5<\/sup><\/a><\/span><br \/>\n\uc608\ub97c \ub4e4\uc5b4 \ub2e4\ud56d\uc2dd \\(-x+2x^{2020}+2\\)\ub97c \ub0b4\ub9bc\ucc28\uc21c\uacfc \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[<br \/>\n2x^{2020}-x+2,\\quad 2-x+2x^{2020}<br \/>\n\\]<br \/>\n\ubb38\uc790\uac00 \ub450 \uac1c \uc774\uc0c1\uc788\ub294 \ub2e4\ud56d\uc2dd\uc740 \ud558\ub098\uc758 \ubb38\uc790\ub97c \uae30\uc900\uc73c\ub85c \uc815\ub9ac\ud55c\ub2e4. \uc774\ub54c \uae30\uc900\uc73c\ub85c \uc0bc\ub294 \ubb38\uc81c\ub97c \uc81c\uc678\ud55c \ub2e4\ub978 \ubb38\uc790\ub294 \ubaa8\ub450 \uc0c1\uc218\ub85c \uc0dd\uac01\ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ub2e4\ud56d\uc2dd \\(-xy+x^{2}+a^{3}y^{2}+x\\)\ub97c \\(x\\)\ub97c \uae30\uc900\uc73c\ub85c \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uba74<br \/>\n\\[<br \/>\nx^{2}+(-y+1)x+a^{3}y^{2}<br \/>\n\\]<br \/>\n\uc774\uba70 \uc774\ub97c \ub2e4\uc2dc \\(y\\)\uc5d0 \uad00\ud55c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uba74<br \/>\n\\[<br \/>\nx^{2}+x-xy+a^{3}y^{2}<br \/>\n\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<p> <span class=\"definition\"> \ubcf4\uae30 <\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(x^2+2xy^{2}+7y-3\\)\uc744 \ubb38\uc790 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \uc0dd\uac01\ud588\uc744 \ub54c\ub294 \\(2xy^{2}\\)\ub294 \\(1\\)\ucc28\ud56d\uc774\uba70 \\(1\\)\ucc28\ud56d\uc758 \uacc4\uc218\ub294 \\(2y^{2}\\)\uc774\ub2e4. \uadf8\ub7ec\ub098 \ubcc4\ub2e4\ub978 \uc5b8\uae09 \uc5c6\uc774 \uc774 \ub2e4\ud56d\uc2dd\uc774 \uba87 \ucc28 \ub2e4\ud56d\uc2dd\uc778\uac00 \ubb3c\uc5c8\uc744 \ub54c\ub294 (\\(x, y\\)\uc5d0 \ub300\ud55c) \\(3\\)\ucc28\uc2dd\uc774\ub77c\uace0 \ub2f5\ud558\ub294 \uac83\uc774 \uc88b\ub2e4.\n<\/p>\n<p>\n\ub2e4\ud56d\uc2dd\uc758 \ub367\uc148\uc740  \uc2dd\uc744 \ub208\uce58\uaecf \uc798 \uc815\ub9ac\ud574\uc11c<span id='easy-footnote-6-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-6-4351' title='\ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc608\uc058\uac8c \uc815\ub9ac\ud558\ub294 \uc13c\uc2a4\ub294 \uae30\ubcf8'><sup>6<\/sup><\/a><\/span>  \ub3d9\ub958\ud56d\ub07c\ub9ac \uacc4\uc0b0\ud558\uba74 \ub41c\ub2e4. \ub2e4\ud56d\uc2dd\uc758 \ube84\uc148\uc740 \ube7c\ub294 \ub2e4\ud56d\uc2dd\uc758 \uac01 \ud56d\uc758 \ubd80\ud638\ub97c \ubc14\uafb8\uc5b4 \ub354\ud558\uc5ec \uacc4\uc0b0\ud55c\ub2e4. \ubb3c\ub860 \uc9c0\uae08 \ub2e4\ub8e8\uace0 \uc788\ub294 \ubb38\uc790\ub294 \uc2e4\uc218 \ud639\uc740 \ubcf5\uc18c\uc218\ub97c \ub300\uc2e0\ud558\uc5ec \ub098\ud0c0\ub0b8 \uac83\uc774\ub2c8 \uacb0\ud569\ubc95\uce59\uacfc \ubd84\ubc30\ubc95\uce59\uacfc \uac19\uc740<span id='easy-footnote-7-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-7-4351' title='\ubb34\ucc99 \ub2f9\uc5f0\ud55c \uc774\uc57c\uae30\uc9c0\ub9cc \ubb38\uc790\ub97c \uacc4\uc0b0\ud568\uc5d0 \uc788\uc5b4, \uadf8 \ubb38\uc790\uac00 \ubb34\uc5c7\uc744 \ub098\ud0c0\ub0b4\ub294\uac00\uc5d0  \uacc4\uc0b0\uc5d0 \uad00\ud55c \uc5b4\ub5a4 \uc131\uc9c8\ub4e4\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294\uc9c0\uac00 \ub2ec\ub824\uc788\ub2e4.'><sup>7<\/sup><\/a><\/span><br \/>\n \uc5f0\uc0b0\uc5d0 \uad00\ud55c \uc88b\uc740 \uc131\uc9c8\ub4e4\uc744 \uc801\uc808\ud788 \uc774\uc6a9\ud558\uc5ec \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\uc608\ub97c \ub4e4\uc5b4, \ub450 \ub2e4\ud56d\uc2dd \\(2x^{2}+x+1\\)\uacfc \\(5-3x-x^{2}+3x^{3}\\)\uc758 \ub367\uc148\uc740<br \/>\n\\begin{align*}<br \/>\n(2x^{2}+x+1) + (5-3x-x^{2}+3x^{3}) &#038; = 2x^{2}+x+1 + 5-3x-x^{2}+3x^{3} \\\\<br \/>\n&#038; = 3x^{3} +(2-1)x^{2}+(1-3)x + (1+5) \\\\<br \/>\n&#038; = 3x^{3}+x^{2}-2x+6<br \/>\n\\end{align*}<br \/>\n\uc73c\ub85c, \ube84\uc148\uc740<br \/>\n\\begin{align*}<br \/>\n(2x^{2}+x+1) &#8211; (5-3x-x^{2}+3x^{3}) &#038; = (2x^{2}+x+1) +( -5+3x+x^{2}-3x^{3}) \\\\<br \/>\n&#038;= 2x^{2}+x+1  -5+3x+x^{2}-3x^{3} \\\\<br \/>\n&#038; = &#8211; 3x^{3} +(2+1)x^{2}+(1+3)x + (1-5) \\\\<br \/>\n&#038; = -3x^{3}+3x^{2}+4x-4<br \/>\n\\end{align*}<br \/>\n\ub85c \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4. \ubb3c\ub860 \uc774 \uacc4\uc0b0\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \ub3d9\ub958\ud56d\uc744 \ub9de\ucd94\uc5b4 \uc138\ub85c\uc148\uc73c\ub85c \ud560 \uc218\ub3c4 \uc788\ub2e4.<span id='easy-footnote-8-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-8-4351' title=' \uc0ac\uc2e4 \uc911\uc694\ud55c \uac74, \uac01 \ud56d\uc758 \uacc4\uc218\ub4e4\uc774\ub2c8 \uc138\ub85c\uc148\uc5d0 \ubb38\uc790\ub97c \ub2e4 \uc368\ub193\uc744 \ud544\uc694\ub294 \uc5c6\uc5b4\ubcf4\uc778\ub2e4.  \uc789\ud06c\ub97c \ub0ad\ube44\ud55c \uac74 \uc544\ub2d0\uae4c&amp;#8230;'><sup>8<\/sup><\/a><\/span>\n<\/p>\n<p><!-- \\begin{center}\n\\begin{tabular}{crrrr}\n                         &        & \\)2x^2\\) & \\)+x\\)  & \\)+1\\) \\\\\n\\multicolumn{1}{l|}{\\)+\\)} & \\)3x^3\\) & \\)-x^2\\) & \\)-3x\\) & \\)+5\\) \\\\ \\cline{2-5} \n                         & \\)3x^3\\) & \\)+x^2\\) & \\)-2x\\) & \\)+6\\)\n\\end{tabular}\n\\qquad \n\\begin{tabular}{crrrr}\n                         &        & \\)2x^2\\) & \\)+x\\)  & \\)+1\\) \\\\\n\\multicolumn{1}{l|}{\\)-\\)} & \\)3x^3\\) & \\)-x^2\\) & \\)-3x\\) & \\)+5\\) \\\\ \\cline{2-5} \n                         & \\)-3x^3\\) & \\)+3x^2\\) & \\)+4x\\) & \\)-4\\)\n\\end{tabular}\n\\end{center}\n--><br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-301.png\" alt=\"\" width=\"500\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.1<\/span><br \/>\n\uc8fc\uc5b4\uc9c4 \ub450 \ub2e4\ud56d\uc2dd \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec \\(A+B\\)\uc640 \\(A-B\\)\ub97c \uac01\uac01 \uad6c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(A=3a^{3}-2a-1,\\quad B=7a^{3}-3a^{2}+2a+4\\) <\/li>\n<li> \\(A=x^{2}+2xy+5y^{2},\\quad B=2x^{2}-4xy+2y^{2}\\) <\/li>\n<\/ol>\n<p>\n\uc720\uc81c 3.1\uc758 \uacb0\uacfc\ub97c \ubcf4\uace0 \uc7a0\uc2dc \uc0dd\uac01\ud574\ubcf4\uba74  \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569\uc740 \ub367\uc148\uc5d0 \ub300\ud558\uc5ec \ub2eb\ud600 \uc788\uc74c\uc744 \uc54c \uc218 \uc788\ub2e4. \uadf8\ub9ac\uace0 \ub2e4\ud56d\uc2dd\uc758 \ub367\uc148\uc5d0 \uc788\uc5b4\uc11c\ub3c4 \ub367\uc148\uc5d0 \ub300\ud55c  \uacb0\ud569\ubc95\uce59 \ubc0f \uad50\ud658\ubc95\uce59\uc774 \uc131\ub9bd\ud568\uc744 \uc54c \uc218 \uc788\ub2e4. \ub610\ud55c \\(A\\)\uac00 \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd\uc77c \ub54c, \\(A+0=0+A=A\\)\uc774\ubbc0\ub85c \ub2e4\ud56d\uc2dd \\(0\\)\uc740 \ub2e4\ud56d\uc2dd\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0\uc774\ub2e4. \uadf8\ub9ac\uace0 \ub2e4\ud56d\uc2dd \\(A\\)\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc774 \\(-A\\)\uc778 \uac83\ub3c4 \ubc14\ub85c \uc54c \uc218 \uc788\ub2e4.  \ub2e4\ud56d\uc2dd\uc758 \ub367\uc148\uc5d0 \uad00\ud55c \uae30\ubcf8 \uc131\uc9c8\uc744 \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<span id='easy-footnote-9-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-9-4351' title=' \ub367\uc148\uc758 \uc5ed\uc6d0\uc774 \uc788\uc73c\ub2c8 \ube84\uc148\uc744 \uc798 \uc815\uc758\ud560 \uc218 \uc788\ub2e4.'><sup>9<\/sup><\/a><\/span>\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Proposition 3.1.1 <\/span> (\ub2e4\ud56d\uc2dd\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \uae30\ubcf8 \uc131\uc9c8) <\/p>\n<ol class=\"parenthesis-roman\">\n<li> \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd \\(A, B, C\\)\uc5d0 \ub300\ud558\uc5ec  <span class=\"hfill\"> (\uacb0\ud569\ubc95\uce59)  <\/span> <br \/>\n \\(\\phantom{\uc784\uc758\uc758 \ub2e4\ud56d\uc2dd}\\)  \\((A+B)+C=A+(B+C)\\) <\/li>\n<li> \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec \\(A+B=B+A\\) <span class=\"hfill\"> (\uad50\ud658\ubc95\uce59) <\/span> <\/li>\n<li> \ub367\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0 \\(0\\)\uc774 \uc788\ub2e4.  <span class=\"hfill\"> (\ud56d\ub4f1\uc6d0) <\/span> <\/li>\n<li> \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd \\(A\\)\ub294 \ub367\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0 \\(-A\\)\ub97c \uac16\ub294\ub2e4. <span class=\"hfill\"> (\uc5ed\uc6d0)  <\/span> <\/li>\n<\/ol>\n<\/div>\n<p>\n\uc774\uc81c \ub2e4\ud56d\uc2dd\uc758 \uacf1\uc148\uc744 \uc0b4\ud3b4\ubcf4\uc790. \ub2e4\ud56d\uc2dd\uc758 \uacf1\uc148\uc740 \ub2e4\ud56d\uc2dd\uc744 \uc804\uac1c\ud558\ub294 \uac83\uacfc \uac19\ub2e4. \ub450 \ub2e4\ud56d\uc2dd\uc758 \uacf1\uc148\uc5d0\uc11c\ub3c4 \uc2dd\uc744 \ub208\uce58\uaecf \uc798 \uc815\ub9ac\ud574\uc11c \uacb0\ud569\ubc95\uce59, \uad50\ud658\ubc95\uce59 \uadf8\ub9ac\uace0 \uacf1\uc148\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \ubd84\ubc30\ubc95\uce59\uc744 \uc798 \ud65c\uc6a9\ud558\uc5ec \uacc4\uc0b0\ud558\uba74 \ub41c\ub2e4. \ub2e4\uc74c \uc608\uc81c\ub85c \uc124\uba85\uc744 \ub300\uc2e0\ud55c\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.2<\/span><br \/>\n\ub2e4\uc74c \uc2dd\uc744 \uc804\uac1c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li>   \\((2x^{2}+3x-1)(x+5)\\) <\/li>\n<li>  \\((x+3y-1)(x-2y)\\) <\/li>\n<\/ol>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li> \\begin{align*}<br \/>\n(2x^{2}+3x-1)(x+5)&#038;=2x^{2}(x+5)+3x(x+5)-(x+5) \\\\<br \/>\n&#038;=2x^{3}+10x^{2}+3x^{2}+15x-x-5 \\\\<br \/>\n&#038;= 2x^{3}+13x^{2}+14x-5<br \/>\n\\end{align*} <\/li>\n<li>  \\begin{align*}<br \/>\n(x+3y-1)(x-2y) &#038; = x(x-2y)+3y(x-2y)-(x-2y) \\\\<br \/>\n&#038; = x^{2}-2xy+3xy -6y^{2}-x +2y \\\\<br \/>\n&#038; = x^{2}+xy-6y^{2} -x +2y<br \/>\n\\end{align*}\n<\/li>\n<\/ol>\n<p><span class=\"qed\"><\/span><\/p>\n<p><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.3<\/span><br \/>\n\uc704\uc758 \uc608\uc81c 3.2\uc758 \ud480\uc774\uc5d0\uc11c \uac01 \uc904\uc758 \ub4f1\ud638\uc5d0 \uc0ac\uc6a9\ud55c \uc131\uc9c8\uc774 \ubb34\uc5c7\uc778\uc9c0 \uc124\uba85\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.4<\/span><br \/>\n\ub2e4\uc74c \uc2dd\uc744 \uc804\uac1c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li>  \\((a^{2}-2a-1)(a^{2}+4)\\) <\/li>\n<li>  \\((x+2y-2)(x-y-3)\\) <\/li>\n<\/ol>\n<p>\n\ub2e4\ud56d\uc2dd\uc758 \uacf1\uc148\uc740 \ubd84\ubc30\ubc95\uce59\uc744 \uc774\uc6a9\ud558\uc5ec \uc804\uac1c\ud560 \uc218\ub3c4 \uc788\uc9c0\ub9cc \ud2b9\ubcc4\ud55c \ubaa8\uc591\uc758 \uacf1\uc148\uc740 \uc911\ud559\uad50\uc5d0\uc11c \ubc30\uc6b4 \ub2e4\uc74c \uacf1\uc148 \uacf5\uc2dd\ub4e4\uc744 \uc774\uc6a9\ud558\uba74 \ud3b8\ub9ac\ud558\ub2e4.<br \/>\n\\begin{align*}<br \/>\n(a+b)^{2} &#038; =a^{2} +2ab+b^{2} \\\\<br \/>\n(a-b)^{2} &#038; =a^{2} -2ab+b^{2} \\\\<br \/>\n(a+b)(a-b) &#038;=a^{2} -b^{2} \\\\<br \/>\n(x+a)(x+b) &#038; =x^{2} +(a+b)x+ab \\\\<br \/>\n(ax+b)(cx+d) &#038; =acx^{2} +(ad+bc)x+bd<br \/>\n\\end{align*}\n<\/p>\n<p>\n\uc704 \uacf5\uc2dd\uc744 \uc774\uc6a9\ud558\uc5ec \uc880 \ub354 \ubcf5\uc7a1\ud55c \uc2dd\uc744 \uc804\uac1c\ud558\uc5ec \ubcf4\uc790. \uc608\ub97c \ub4e4\uc5b4, \uacf1\uc148 \uacf5\uc2dd \\((a+b)^{2} =a^{2} +2ab+b^{2}\\)\uc744 \uc774\uc6a9\ud558\uc5ec \\((a+b+c)^{2}\\)\uacfc  \\((a+b)^{3}\\)\uc744 \uc804\uac1c\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\begin{align*}<br \/>\n(a+b+c)^{2} &#038; = \\left( (a+b)+c\\right)^{2} \\\\<br \/>\n&#038; =(a+b)^{2} +2(a+b)c+c^{2} \\\\<br \/>\n&#038; =a^{2} +2ab+b^{2} +2ac+2bc+c^{2} \\\\<br \/>\n&#038; =a^{2} +b^{2} +c^{2} +2ab+2bc+2ca, \\\\<br \/>\n (a+b)^{3} &#038; =(a+b)^{2} (a+b) \\\\<br \/>\n&#038; =(a^{2} +2ab+b^{2} )(a+b) \\\\<br \/>\n&#038; =a^{3} +a^{2} b+2a^{2} b+2ab^{2} +ab^{2} +b^{3}  \\\\<br \/>\n&#038; =a^{3} +3a^{2} b+3ab^{2} +b^{3}<br \/>\n\\end{align*}<br \/>\n\ud55c\ud3b8, \uc704 \ub4f1\uc2dd\uc5d0\uc11c \\(b\\) \ub300\uc2e0 \\(-b\\)\ub97c \ub300\uc785\ud558\uba74<br \/>\n\\[<br \/>\n(a-b)^{3} =a^{3} -3a^{2} b+3ab^{2} -b^{3}<br \/>\n\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.5<\/span><br \/>\n\ub2e4\uc74c \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud568\uc744 \ubcf4\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li>  \\((a+b)\\left(a^2-ab+b^{2}\\right)=a^{3}+b^{3}\\) <\/li>\n<li> \\((a-b)\\left(a^{2}+ab+b^{2}\\right)=a^{3}-b^{3}\\) <\/li>\n<\/ol>\n<p>\n\uc774\ub85c\ubd80\ud130 \ub2e4\uc74c\uacfc \uac19\uc740 \uacf5\uc2dd\uc744 \uc5bb\ub294\ub2e4.<span id='easy-footnote-10-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-10-4351' title=' \uc774\uc815\ub3c4\uc758 \uacf5\uc2dd\uc740 \uc329\uae30\ucd08!'><sup>10<\/sup><\/a><\/span>\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 3.1.2 <\/span> (\uacf1\uc148 \uacf5\uc2dd)<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\((a+b+c)^2 =a^2 +b^2 +c^2 +2ab +2bc +2ca \\) <\/li>\n<li> \\((a+b)^3 =a^3 +3a^2 b +3ab^2 +b^3,\\) <br \/>\n \t\t \\((a-b)^3=a^3 -3a^2 b +3ab^2 -b^3\\) <\/li>\n<li> \\((a+b)(a^2 -ab +b^2) =a^3 +b^3,\\) <br \/>\n\t\t \\((a-b)(a^2 +ab +b^2 ) =a^3 -b^3\\) <\/li>\n<\/ol>\n<\/div>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.6<\/span><br \/>\n\uacf1\uc148 \uacf5\uc2dd\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \uc2dd\uc744 \uc804\uac1c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li>  \\((a+b-c)^{2}\\) <\/li>\n<li>  \\((x+2)^{3}\\) <\/li>\n<\/ol>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li> \\begin{align*}<br \/>\n(a+b-c)^{2}&#038;=a^{2} +b^{2} +(-c)^{2} +2\\cdot a\\cdot b \\\\<br \/>\n&#038;\\phantom{MMMMMMMM} +2\\cdot b \\cdot (-c) +2\\cdot (-c)\\cdot a \\\\<br \/>\n&#038; =a^{2} +b^{2} +c^{2} +2ab-2bc-2ca<br \/>\n\\end{align*} <\/li>\n<li> \\begin{align*}<br \/>\n (x+2)^{3} &#038; =x^{3} +3\\cdot x^{2} \\cdot 2+3\\cdot x\\cdot 2^{2} +2^{3}\\\\<br \/>\n &#038;  =x^{3} +6x^{2} +12x+8<br \/>\n \\end{align*} <\/li>\n<\/ol>\n<p><span class=\"qed\"><\/span><\/p>\n<p><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.7<\/span><br \/>\n\uacf1\uc148 \uacf5\uc2dd\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \uc2dd\uc744 \uc804\uac1c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\((2x-y+3)^{2}\\) <\/li>\n<li> \\((2a-3)^{3} \\) <\/li>\n<li> \\((x+2)(x^{2} -2x+4)\\) <\/li>\n<li> \\((x-3y)(x^{2} +3xy+9y^{2} )\\) <\/li>\n<\/ol>\n<p>\n\uc9c0\uae08\uae4c\uc9c0\uc758 \uacc4\uc0b0\uc5d0\uc11c \uc54c \uc218 \uc788\ub4ef\uc774 \ub450 \ub2e4\ud56d\uc2dd\uc758 \uacf1\uc148\uc758 \uacb0\uacfc\ub294 \ud56d\uc0c1 \ub2e4\ud56d\uc2dd\uc774\ubbc0\ub85c \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569\uc740 \uacf1\uc148\uc5d0 \ub300\ud558\uc5ec \ub2eb\ud600 \uc788\ub2e4. \uadf8\ub9ac\uace0 \ub2e4\ud56d\uc2dd\uc5d0\uc11c\ub3c4 \uc2e4\uc218\uc640 \ub9c8\ucc2c\uac00\uc9c0\ub85c \uacf1\uc148\uc5d0 \ub300\ud558\uc5ec \uad50\ud658\ubc95\uce59\uacfc \uacb0\ud569\ubc95\uce59\uc774 \uc131\ub9bd\ud558\uba70, \uacf1\uc148\uc758 \ub367\uc148\uc5d0 \ub300\ud55c \ubd84\ubc30\ubc95\uce59\uc774 \uc131\ub9bd\ud55c\ub2e4. \ub610\ud55c \\(1\\)\uc740 \uacf1\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0\uc774\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 3.1.3 <\/span> (\ub2e4\ud56d\uc2dd\uc758 \uacf1\uc148\uc5d0 \ub300\ud55c \uae30\ubcf8 \uc131\uc9c8)<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd \\(A, B\\)\uc5d0 \ub300\ud558\uc5ec \\(AB=BA\\) <span class=\"hfill\"> (\uad50\ud658\ubc95\uce59) <\/span> <\/li>\n<li> \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd \\(A, B, C\\)\uc5d0 \ub300\ud558\uc5ec \\((AB)C=A(BC)\\) <span class=\"hfill\"> (\uacb0\ud569\ubc95\uce59) <\/span> <\/li>\n<li>  \uc784\uc758\uc758 \ub2e4\ud56d\uc2dd \\(A, B, C\\)\uc5d0 \ub300\ud558\uc5ec   <span class=\"hfill\"> (\ubd84\ubc30\ubc95\uce59<span id='easy-footnote-11-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-11-4351' title=' \ubd84\ubc30\ubc95\uce59\uc758 \uacbd\uc6b0 &amp;#8216;\uacf1\uc148\uc5d0 \ub300\ud55c \uc131\uc9c8&amp;#8217;\uc774\ub77c\uae30\ubcf4\ub2e8 &amp;#8216;\ub367\uc148\uacfc \uacf1\uc148\uc744 \uc5f0\uacb0\uc9d3\ub294 \uc131\uc9c8&amp;#8217;\uc774\ub77c \ud574\uc57c\uaca0\uc9c0\ub9cc&amp;#8230; '><sup>11<\/sup><\/a><\/span>)  <\/span> <br \/> <br \/>\n \\(\\phantom{\uc784\uc758\uc758 \ub2e4\ud56d\uc2dd}\\) \\(A(B+C)=AB+AC\\)  <\/li>\n<li> \uacf1\uc148\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc6d0 \\(1\\)\uc774 \uc788\ub2e4. <span class=\"hfill\"> (\ud56d\ub4f1\uc6d0) <\/span> <\/li>\n<\/ol>\n<\/div>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.8<\/span><br \/>\n\ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0 \uc788\ub294 \uc6d0\uc18c \uc911 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc744 \uac16\ub294 \uc6d0\uc18c\ub294 \ubb34\uc5c7\uc778\uc9c0 \uc124\uba85\ud558\uc5ec\ub77c.\n<\/p>\n<p>\uc720\uc81c 3.8\uc5d0\uc11c \uc54c \uc218 \uc788\ub4ef\uc774 \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c\uc758 \uacf1\uc148\uc5d0\uc11c\ub294 \uacf1\uc148\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc744 \uac16\uc9c0 \uc54a\ub294 \uc6d0\uc18c\uac00 \ub300\ubd80\ubd84\uc774\ub77c \ud560 \uc218 \uc788\ub2e4. \uc774\ub294 \ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c\uc758 \ub098\ub217\uc148\uc744 \uc720\ub9ac\uc218, \uc2e4\uc218, \ubcf5\uc18c\uc218\uc758 \uacbd\uc6b0\uc5d0\uc11c\ucc98\ub7fc \ud560 \uc218\ub294 \uc5c6\uc74c\uc744 \ub73b\ud55c\ub2e4. \uadf8\ub7ec\ub098 \ub2e4\ud56d\uc2dd\uc758 \ub098\ub217\uc148\uc744 \uc815\uc218\uc758 \ub098\ub217\uc148\uc5d0\uc11c\ucc98\ub7fc \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\ub294 \uacfc\uc815\uc73c\ub85c \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \uc989 \uc8fc\uc5b4\uc9c4 \ub2e4\ud56d\uc2dd\uc744 \\(0\\)\uc774 \uc544\ub2cc \ub2e4\ud56d\uc2dd\uc73c\ub85c \ub098\ub20c \ub54c, \uac01 \ub2e4\ud56d\uc2dd\uc744 \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uc5ec \uc815\uc218\uc758 \ub098\ub217\uc148\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uacc4\uc0b0\ud55c\ub2e4.\n <\/p>\n<p>\n \uc608\ub97c \ub4e4\uc5b4 \\((2x^{2}+5x-5)\\div (x+3)\\)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uacc4\uc0b0\ud55c\ub2e4.\n<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-302.png\" alt=\"\" width=\"280\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><\/p>\n<p>\n\uc704\uc758 \uacc4\uc0b0\uc5d0\uc11c, \uc815\uc218\uc758 \ub098\ub217\uc148\uc5d0\uc11c \uadf8\ub7ac\ub358 \uac83\ucc98\ub7fc, \\(2x-1\\)\uc744 <span class=\"defined\">\ubaab<\/span>\uc774\ub77c \ubd80\ub974\uace0 \\(-2\\)\uc744 <span class=\"defined\">\ub098\uba38\uc9c0<\/span>\ub77c \ubd80\ub974\uba74 \uadf8\ub7f4\ub4ef \ud558\ub2e4.<span id='easy-footnote-12-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-12-4351' title=' \uc815\ud655\ud558\uac8c\ub294 \\(2x^{2} +5x-5\\)\ub97c \\(x+3\\)\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ubaab\uacfc \ub098\uba38\uc9c0. '><sup>12<\/sup><\/a><\/span> \uadf8\ub9ac\uace0 \uc815\uc218\uc758 \ub098\ub217\uc148\uc5d0\uc11c\ucc98\ub7fc \ub098\ub217\uc148\uc758 \uacb0\uacfc\ub97c<br \/>\n\\[<br \/>\n2x^{2} +5x-5=(x+3)(2x-1)-2<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\uc77c\ubc18\uc801\uc73c\ub85c \ub2e4\ud56d\uc2dd\uc758 \ub098\ub217\uc148\uc5d0\uc11c \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 3.1.4 <\/span> (\ub2e4\ud56d\uc2dd\uc758 \ub098\ub217\uc148\uc5d0 \ub300\ud55c \uc131\uc9c8: \uc720\ud074\ub9ac\ub4dc \uc54c\uace0\ub9ac\uc998)<br \/>\n\ub2e4\ud56d\uc2dd \\(A\\)\uc640 \\(0\\)\uc774 \uc544\ub2cc \ub2e4\ud56d\uc2dd \\(B\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nA=BQ+R,\\quad \\mbox{\ub2e8, \\(\\deg(R) < \\deg(B)\\)}\n\\]\n\uc778 \ub2e4\ud56d\uc2dd \\(Q, R\\)\uc774 \uc874\uc7ac\ud55c\ub2e4. [efn_note] \ub2e4\ud56d\uc2dd \\(A\\)\uc758 \ucc28\uc218\ub97c \\(\\deg(A)\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.[\/efn_note]\n<\/p>\n<\/div>\n<p>\n\ud2b9\ud788, \\(R=0\\)\uc774\uba74 \\(A=BQ\\)\uc774\ub2e4. \uc774 \uacbd\uc6b0 \uc815\uc218\uc640 \ub9c8\ucc2c\uac00\uc9c0\ub85c \\(A\\)\ub294 \\(B\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c4\ub2e4\uace0 \ub9d0\ud55c\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.9<\/span><br \/>\n\ub2e4\uc74c \ub098\ub217\uc148\uc758 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uace0, \uadf8 \uacb0\uacfc\ub97c \\(A=BQ+R\\) \uaf34\ub85c \ub098\ud0c0\ub0b4\uc5b4\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\((2x^{2} +5x-2)\\div (2x+1)\\)  <\/li>\n<li> \\((3x^{3} +5x+2)\\div (x^{2} -1)\\) <\/li>\n<li> \\((x^{3} -3x^{2} -6x+8)\\div (x-2)\\)  <\/li>\n<li> \\((x^{3} -3x^{2} +x-1)\\div (x^{2} -2x-3)\\) <\/li>\n<\/ol>\n<p>\n\ub2e4\ud56d\uc2dd\uc744 \\(x-a\\)\uc640 \uac19\uc740 \uc77c\ucc28\uc2dd\uc73c\ub85c \ub098\ub20c \ub54c\uc5d0\ub294 \uc9c1\uc811 \ub098\ub204\uc9c0 \uc54a\uace0 \uacc4\uc218\ub9cc\uc744 \uc774\uc6a9\ud558\uc5ec \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\ub294 \ubc29\ubc95\uc774 \uc788\ub2e4.<br \/>\n\uc608\ub97c \ub4e4\uc5b4, \\(3x^{3} -3x^{2} +2x+4\\)\ub97c \\(x-2\\)\ub85c \uc9c1\uc811 \ub098\ub204\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<span id='easy-footnote-13-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-13-4351' title='\uc5ed\uc2dc \uacc4\uc218\ub9cc\uc744 \uc774\uc6a9\ud558\ub294 \uac83\uc774 \uc808\uc57d\uc815\uc2e0\uc5d0 \ubd80\ud569\ud558\ub294 \uac83\uc774\ub2e4!'><sup>13<\/sup><\/a><\/span>\n<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-303.png\" alt=\"\" width=\"550\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><\/p>\n<p>\n\ub530\ub77c\uc11c \\(3x^{3} -3x^{2} +2x+4\\)\ub97c \\(x-2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ubaab\uc740 \\(3x^{2} +3x+8\\)\uc774\uace0 \ub098\uba38\uc9c0\ub294 \\(20\\)\uc774\ub2e4. \uc774\ub54c, \uc704 \uacc4\uc0b0 \uacfc\uc815\uc5d0\uc11c \uacc4\uc218\ub9cc \uc0dd\uac01\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95 \uc73c\ub85c \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uac04\ub2e8\ud788 \uad6c\ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-304.png\" alt=\"\" width=\"330\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><\/p>\n<p>\n\uc774\uc640 \uac19\uc774 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\ub294 \ubc29\ubc95\uc744 <span class=\"defined\">\uc870\ub9bd\uc81c\ubc95<\/span>\uc774\ub77c\uace0 \ud55c\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.10<\/span><br \/>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \ub098\ub217\uc148\uc758 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.<br \/>\n\\[<br \/>\n(x^{3} +3x^{2} -7)\\div(x+1)<br \/>\n\\]\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uacc4\uc0b0\ud55c\ub2e4.<span id='easy-footnote-14-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-14-4351' title='\ub098\ub204\uc5b4\uc9c0\ub294 \ub2e4\ud56d\uc2dd\uc758 \uacc4\uc218\ub97c \ub098\uc5f4\ud560 \ub54c, \ub2e4\ud56d\uc2dd\uc758 \ucc28\uc218\ubcc4\ub85c &lt;span class=&quot;defined&quot;&gt;\ubaa8\ub4e0 \uacc4\uc218\ub97c \ube60\uc9d0\uc5c6\uc774 \uc368\uc57c\ud568&lt;\/span&gt;\uc5d0 \uc720\uc758\ud558\uc790. \uc989, \uacc4\uc218\uac00 \\(0\\)\uc77c \ub54c\uc5d0\ub3c4 \\(0\\)\uc744 \uc4f0\ub294 \uac83\uc744 \ube60\ub728\ub9ac\uc9c0 \ub9d0\uc790.'><sup>14<\/sup><\/a><\/span><br \/>\n<!-- \n\\begin{center}\n\\polyhornerscheme[x=-1,resultbottomrule=true,resultleftrule=true]{x^3 +3x^2-7}\n\\end{center}\n--><br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-305.png\" alt=\"\" width=\"200\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n\ub530\ub77c\uc11c \uad6c\ud558\ub294 \ubaab\uc740 \\(x^{2} +2x-2\\)\uc774\uace0 \ub098\uba38\uc9c0\ub294 \\(-5\\)\uc774\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.11<\/span><br \/>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \ub098\ub217\uc148\uc758 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\((2x^{3} +x^{2} +3x-2)\\div(x-1)\\)  <\/li>\n<li> \\((x^{4} -2x^{2} +x+1)\\div(x+2)\\) <\/li>\n<\/ol>\n<p>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\ud56d\uc2dd\uc744 \uc77c\ucc28\ud56d\uc758 \uacc4\uc218\uac00 \\(1\\)\uc774 \uc544\ub2cc \uc77c\ucc28\uc2dd\uc73c\ub85c \ub098\ub20c \ub54c\uc758 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\ub294 \ubc29\ubc95\uc744 \uc54c\uc544\ubcf4\uc790.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.12<\/span><br \/>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \ub098\ub217\uc148\uc758 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.<br \/>\n\\[<br \/>\n(2x^{3} -5x^{2} -2x+3)\\div(2x-1)<br \/>\n\\]\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \\(2x^{3} -5x^{2} -2x+3\\)\uc744 \uc77c\ucc28\uc2dd \\(x-\\frac{1}{2}\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uba74<br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-306.png\" alt=\"\" width=\"200\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n\uc73c\ub85c \ubaab\uc740 \\(2x^{2} -4x-4\\)\uc774\uace0 \ub098\uba38\uc9c0\ub294 \\(1\\)\uc774\ubbc0\ub85c <!--[efn_note] \\polyhornerscheme[x=1\/2,resultbottomrule=true,resultleftrule=true]{2x^3 -5x^2 -2x+3} [\/efn_note] --><br \/>\n\\begin{align*}<br \/>\n2x^{3} -5x^{2} -2x+3&#038; =\\left(x-\\frac{1}{2}\\right)(2x^{2} -4x-4)+1 \\\\<br \/>\n&#038; =(2x-1)\\left(x^{2} -2x-2\\right)+1<br \/>\n\\end{align*}<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c  \ubaab\uc740 \\(x^{2} -2x-2\\)\uc774\uace0 \ub098\uba38\uc9c0\ub294 \\(1\\)\uc774\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\uc704\uc758 \uacb0\uacfc\ub85c\ubd80\ud130 \uc5b4\ub5a4 \ub2e4\ud56d\uc2dd\uc744 \uc77c\ucc28\uc2dd \\(ax-b\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ubaab\uc740 \uadf8 \ub2e4\ud56d\uc2dd\uc744 \uc77c\ucc28\uc2dd \\(x-\\frac{b}{a}\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ubaab\uc758 \\(\\frac{1}{a}\\)\uc774 \ub428\uc744 \uc54c \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.13<\/span><br \/>\n\uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \ub098\ub217\uc148\uc758 \ubaab\uacfc \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\((2x^{3} -3x+2)\\div(2x+1)\\)  <\/li>\n<li> \\((4x^{4} +3x^{2} -2x+1)\\div(2x-3)\\) <\/li>\n<\/ol>\n<h4> \ud56d\ub4f1\uc2dd\uacfc \ub098\uba38\uc9c0\uc815\ub9ac <\/h4>\n<p>\n\ubb38\uc790\uc5d0 \uc5b4\ub5a4 \uac12\uc744 \ub300\uc785\ud558\uc5ec\ub3c4 \ud56d\uc0c1 \uc131\ub9bd\ud558\ub294 \ub4f1\uc2dd\uc744 \uadf8 \ubb38\uc790\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\ub77c\uace0 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4,<br \/>\n\\[<br \/>\n(a+b)^{3} =a^{3} +3a^{2} b+3ab^{2} +b^{3}<br \/>\n\\]<br \/>\n\uacfc \uac19\uc740 \uacf1\uc148 \uacf5\uc2dd\uc5d0\uc11c \ub4f1\uc7a5\ud55c \ub4f1\uc2dd\uc740 \ubaa8\ub450 \ud56d\ub4f1\uc2dd\uc774\ub2e4.\n<\/p>\n<p>\n\ub4f1\uc2dd \\(ax+b=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub420 \uc870\uac74\uc744 \uc54c\uc544\ubcf4\uc790. \ub4f1\uc2dd \\(ax+b=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\uba74 \\(x\\)\uc5d0 \uc5b4\ub5a4 \uac12\uc744 \ub300\uc785\ud574\ub3c4 \ub4f1\ud638\uac00 \uc131\ub9bd\ud55c\ub2e4. \ub530\ub77c\uc11c \\(x=0, x=1\\)\uc744 \uac01\uac01 \ub300\uc785\ud558\uba74 \\(b=0, a+b=0\\)\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\na=b=0<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uc5ed\uc73c\ub85c \\(a=b=0\\)\uc774\uba74 \ub4f1\uc2dd \\(ax+b=0\\)\uc740 \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \ud56d\uc0c1 \uc131\ub9bd\ud55c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ub4f1\uc2dd \\(ax+b=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub418\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(a=b=0\\)\uc774\ub2e4.\n<\/p>\n<p>\n\uc774\uc81c, \ub4f1\uc2dd \\(ax^{2}+bx+c=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub420 \uc870\uac74\uc744 \uc54c\uc544\ubcf4\uc790. \ub4f1\uc2dd \\(ax^{2} +bx+c=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\uba74 \\(x=-1, x=0, x=1\\)\uc744 \uac01\uac01 \ub300\uc785\ud558\uc5ec<br \/>\n\\[<br \/>\na-b+c=0,\\quad c=0, \\quad a+b+c=0<br \/>\n\\]<br \/>\n\uc744 \uc5bb\ub294\ub2e4. \uc774 \uc138 \uc2dd\uc744 \uc5f0\ub9bd\ud558\uc5ec \ud480\uba74<br \/>\n\\[<br \/>\na=b=c=0<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uc5ed\uc73c\ub85c \\(a=b=c=0\\)\uc774\uba74 \ub4f1\uc2dd \\(ax^{2} +bx+c=0\\)\uc740 \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \ud56d\uc0c1 \uc131\ub9bd\ud55c\ub2e4. \ub530\ub77c\uc11c \ub4f1\uc2dd \\(ax^{2}+bx+c=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub418\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(a=b=c=0\\)\uc774\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 3.1.5 <\/span> (\ud56d\ub4f1\uc2dd\uc758 \uae30\ubcf8 \uc131\uc9c8)<br \/>\n\ub4f1\uc2dd \\(ax^{2} +bx+c=0\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub418\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740<br \/>\n\\[<br \/>\na=b=c=0<br \/>\n\\]<br \/>\n\uc778 \uac83\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.14<\/span><br \/>\n\ub4f1\uc2dd \\(ax^{2} +bx+c=a&#8217;x^{2} +b&#8217;x+c&#8217;\\)\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub418\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(a=a&#8217;, b=b&#8217;, c=c&#8217;\\)\uc784\uc744 \ubcf4\uc5ec\ub77c.\n<\/p>\n<p>\n\ud56d\ub4f1\uc2dd\uc5d0\uc11c \uc54c\uc9c0 \ubabb\ud558\ub294 \uacc4\uc218\uc758 \uac12\uc744 \uc815\ud558\ub294 \ubc29\ubc95\uc744 <span class=\"defined\">\ubbf8\uc815\uacc4\uc218\ubc95<\/span>\uc774\ub77c\uace0 \ud55c\ub2e4. \ub300\ud45c\uc801\uc778 \ubbf8\uc815\uacc4\uc218\ubc95\uc5d0\ub294 \uc591\ubcc0\uc758 \uacc4\uc218\ub97c \ube44\uad50\ud558\uc5ec \uacc4\uc218\uc758 \uac12\uc744 \uc815\ud558\ub294 <span class=\"defined\">\uacc4\uc218\ube44\uad50\ubc95<\/span>\uacfc \uc801\uc808\ud55c \uc218\ub97c \ub300\uc785\ud558\uc5ec \uacc4\uc218\uc758 \uac12\uc744 \uc815\ud558\ub294 <span class=\"defined\">\uc218\uce58\ub300\uc785\ubc95<\/span>\uc774 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.15<\/span><br \/>\n\ub4f1\uc2dd \\(x^{2} +4x+3=(x-1)^{2} +a(x-1)+b\\)\uac00 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub418\ub3c4\ub85d \\(a, b\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol(\uacc4\uc218\ube44\uad50\ubc95).<\/span><br \/>\n\uc6b0\ubcc0\uc744 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uba74<br \/>\n\\[<br \/>\nx^{2} +4x+3=x^{2} +(a-2)x+(-a+b+1)<br \/>\n\\]<br \/>\n\uc774\uace0 \uc774 \uc2dd\uc758 \uc591\ubcc0\uc758 \uacc4\uc218\ub97c \uc11c\ub85c \ube44\uad50\ud558\uc5ec<br \/>\n\\[<br \/>\na-2=4, \\quad -a+b+1=3<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \uc774\ub97c \uc5f0\ub9bd\ud558\uc5ec \\(a=6, b=8\\)\ub97c \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span> <\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol(\uc218\uce58\ub300\uc785\ubc95).<\/span><br \/>\n\uc8fc\uc5b4\uc9c4 \uc2dd\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\ubbc0\ub85c \\(x\\)\uc5d0 \uc5b4\ub5a4 \uac12\uc744 \ub300\uc785\ud558\uc5ec\ub3c4 \ub4f1\ud638\uac00 \uc131\ub9bd\ud574\uc57c\ub9cc \ud55c\ub2e4.<br \/>\n\\(x=1\\)\uc744 \ub300\uc785\ud558\uc5ec \\(8=b\\)\ub97c \uc5bb\uace0 \uc774 \uacb0\uacfc\uc640 \\(x=0\\)\uc744 \ub300\uc785\ud558\uc5ec \\(3=1-a+8\\), \uc989 \\(a=6\\)\uc744 \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.16<\/span><br \/>\n\ub2e4\uc74c \ub4f1\uc2dd\uc774 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774 \ub418\ub3c4\ub85d \\(a, b, c\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c. <\/p>\n<ol class=\"parenthesis\">\n<li> \\( (x+a)(x+2)=x^{2} +bx+2\\) <\/li>\n<li> \\( 2x^{2} +3x+7=a(x+1)^{2} +b(x+1)+c\\) <\/li>\n<\/ol>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.17<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(x^{3} +ax^{2} +bx+5\\)\ub97c \\(x^{2} -x+2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\uac00 \\(2x+3\\)\uc774 \ub418\ub3c4\ub85d \\(a, b\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol(1).<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(x^{3}+ax^{2}+bx+5\\)\ub97c \\(x^{2}-x+2\\)\ub85c \ub098\ub204\uc5b4 \ubcf4\uba74<br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-307.png\" alt=\"\" width=\"350\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n \uc73c\ub85c \ub098\uba38\uc9c0\uac00 \\((a+b-1)x+(-2a+3)\\)\uc774\uace0 \ub530\ub77c\uc11c \\((a+b-1)x+(-2a+3)=2x+3\\)\ub97c \uc5bb\ub294\ub2e4.<br \/>\n<!-- [efn_note] \\setstackgap{S}{1.5pt}\n\\stackMath\\def\\stackalignment{r}\n\\(\n\\stackunder{%\n  x^{2}-x+2\\phantom{.} \\stackon[1pt]{\\showdiv{x^{3}+ax^{2}\\phantom{(b-2)}+bx+5 \\phantom{MM 111} }}{ x+(a+1)\\phantom{MMMMMMM\\, ...11} }%\n}{%\n  \\Shortstack[l]{{\\underline{x^{3}- \\phantom{a}x^{2}\\phantom{(b-2)}+2x }} \\ph{\\! }(a+1)x^2\\phantom{..}+(b-2)x+5 {\\ph{\\!}\\underline{(a+1)x^2\\phantom{..}-(a+1)x+2(a+1)}} \\ph{(a+.1)x}(a+b-1)x+(-2a+3) }%\n}\n\\) [\/efn_note] --><br \/>\n\uc774 \ub4f1\uc2dd\uc740 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\na+b-1=2, \\quad -2a+3=3<br \/>\n\\]<br \/>\n\uc774 \uc131\ub9bd\ud558\uace0 \uc774\ub85c\ubd80\ud130 \\(a=0, b=3\\)\ub97c \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span> <\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol(2).<\/span><br \/>\n\ubaab\uc740 \\(x\\)\uc758 \uacc4\uc218\uac00 \\(1\\)\uc778 \uc77c\ucc28\uc2dd\uc77c \uc218\ubc16\uc5d0 \uc5c6\uc73c\ubbc0\ub85c \ubaab\uc744 \\(x+c\\)\ub85c \ub450\uc5b4 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.<br \/>\n\\[<br \/>\nx^{3} +ax^{2} +bx+5=(x^{2} -x+2)(x+c)+(2x+3)<br \/>\n\\]<br \/>\n\uc774 \uc2dd\uc758 \uc591\ubcc0\uc5d0 \\(x=0\\)\uc744 \ub300\uc785\ud558\uc5ec \\(5=2c+3\\), \uc989 \\(c=1\\)\ub97c \uc5bb\ub294\ub2e4. \uc774 \uacb0\uacfc\ub85c\ubd80\ud130 \ud56d\ub4f1\uc2dd<br \/>\n\\[<br \/>\nx^{3} +ax^{2} +bx+5=x^{3} +3x+5<br \/>\n\\]<br \/>\n\ub97c \uc5bb\uc73c\uba70 \uc774\ub85c\ubd80\ud130 \\(a=0\\)\uacfc \\(b=3\\)\uc744 \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.18<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(2x^{3} +ax^{2} +bx-1\\)\uc774 \\(x^{2} +1\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c0\ub3c4\ub85d \\(a, b\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.19<\/span><br \/>\n\ub450 \uc774\ucc28\uc2dd \\(P(x), Q(x)\\)\uc5d0 \ub300\ud558\uc5ec, \ub9cc\uc77c<br \/>\n\\[<br \/>\nP(x)Q(x)=0<br \/>\n\\]<br \/>\n\uac00 \ud56d\ub4f1\uc2dd\uc774\uba74 \\(P(x)=0\\)\uacfc \\(Q(x)=0\\) \uc911 \uc801\uc5b4\ub3c4 \ud558\ub098\ub294 \ud56d\ub4f1\uc2dd\uc784\uc744 \ubcf4\uc5ec\ub77c.\n<\/p>\n<p>\n\uc0c1\ud669\uc5d0 \ub530\ub77c \ub2e4\ud56d\uc2dd\uc758 \ub098\ub217\uc148\uc5d0 \uc788\uc5b4\uc11c \ubaab\ubcf4\ub2e4 \ub098\uba38\uc9c0\uc5d0 \ub354 \uad00\uc2ec\uc744 \uac00\uc9c8 \ub54c\uac00 \uc788\ub2e4. \uc5b4\ub5a4 \ub2e4\ud56d\uc2dd\uc744 \uc77c\ucc28\uc2dd\uc73c\ub85c \ub098\ub20c\ub54c, \ub098\uba38\uc9c0\ub97c \uc27d\uac8c \uad6c\ud558\ub294 \ubc29\ubc95\uc778 \ub098\uba38\uc9c0 \uc815\ub9ac\ub97c \uc54c\uc544\ubcf4\uc790.\n<\/p>\n<p>\n\uc608\ub97c \ub4e4\uc5b4 \ub2e4\ud56d\uc2dd \\(x^{4} -2x^{2} +x-3\\)\uc744 \uc77c\ucc28\uc2dd \\(x-2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\ub97c \uad6c\ud558\ub294 \uacfc\uc815\uc744 \uc54c\uc544\ubcf4\uc790. \uba3c\uc800 \uc9c1\uc811 \ub098\ub217\uc148\uc744 \ud574\ubcf4\uba74<br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-308.png\" alt=\"\" width=\"220\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n<!--\\begin{center}\n\\polyhornerscheme[x=2,resultbottomrule=true,resultleftrule=true]{x^{4} -2x^{2} +x-3}\n\\end{center} --><br \/>\n\ub85c\ubd80\ud130 \ubaab\uc740 \\(x^{3}+2x^{2}+2x+5\\), \ub098\uba38\uc9c0\ub294 \\(7\\)\uc784\uc744 \uc54c \uc218 \uc788\ub2e4. \uc774\uc81c \ubaab\uc774 \uc544\ub2c8\ub77c &#8216;\ub098\uba38\uc9c0&#8217;\uc5d0 \uad00\uc2ec\uc774 \ub354 \uc788\ub2e4\uace0 \uc0dd\uac01\ud558\uace0 \uc774 \uacb0\uacfc, \uc989<br \/>\n\\[<br \/>\nx^{4} -2x^{2} +x-3=(x-2)\\left(x^{3}+2x^{2}+2x+5\\right)+7<br \/>\n\\]<br \/>\n\ub97c \uc0b4\ud3b4\ubcf4\uc790. \uc774 \ub4f1\uc2dd\uc740 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\ubbc0\ub85c \\(x\\)\uc5d0 \uc5b4\ub5a4 \uac12\uc744 \ub300\uc785\ud558\uc5ec\ub3c4 \uc131\ub9bd\ud558\ub294 \uc2dd\uc774\uba70, \ud2b9\ud788 \\(x=2\\)\ub97c \ub300\uc785\ud558\uc5ec\ub3c4 \uc131\ub9bd\ud558\ub294 \uc2dd\uc774\ub2e4.\n<\/p>\n<p>\n\uc77c\ubc18\uc801\uc73c\ub85c \ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \uc77c\ucc28\uc2dd \\(x-a\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ubaab\uc744 \\(Q(x)\\), \ub098\uba38\uc9c0\ub97c \uc0c1\uc218 \\(R\\)\ub85c \ub450\uba74<span id='easy-footnote-15-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-15-4351' title='\ub2e4\ud56d\uc2dd\uc744 \uc77c\ucc28\uc2dd\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub294 \uc0c1\uc218.'><sup>15<\/sup><\/a><\/span><br \/>\n\\[<br \/>\nP(x)=(x-a)Q(x)+R<br \/>\n\\]<br \/>\n\uc774 \uc131\ub9bd\ud558\uba70 \uc774\ub85c\ubd80\ud130<br \/>\n\\[<br \/>\nP(a)=R<br \/>\n\\]<br \/>\n\uacfc \uac19\ub2e4. \uc989 \ub2e4\uc74c\uacfc \uac19\uc740 <span class=\"defined\">\ub098\uba38\uc9c0\uc815\ub9ac<\/span>\uac00 \uc131\ub9bd\ud55c\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 3.1.6 <\/span> (\ub098\uba38\uc9c0\uc815\ub9ac)<br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \uc77c\ucc28\uc2dd \\(x-a\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub294 \\(P(a)\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n<p> <span class=\"definition\"> \ubcf4\uae30 <\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)=x^{4} -3x^{3} +x-4\\)\ub97c \\(x-2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\ub294<br \/>\n\\[<br \/>\nP(2)=2^{4} -3\\cdot 2^{3} +2-4=-10<br \/>\n\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.20<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(2x^{3} +x^{2} -3x+5\\)\ub97c \ub2e4\uc74c \uc77c\ucc28\uc2dd\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c. <\/p>\n<ol class=\"parenthesis\">\n<li> \\( x-1\\)  <\/li>\n<li> \\(x+2\\) <\/li>\n<\/ol>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.21<\/span><br \/>\n\ub2e4\ud56d\uc2dd\uc744 \uc77c\ucc28\uc2dd \\(ax+b\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\uc815\ub9ac\uc5d0 \ub300\ud574 \uc124\uba85\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.22<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(2x^{3} -x^{2} +4x+1\\)\uc744 \\(2x-1\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\ub2e4\uc74c \uc608\uc81c \ubc0f \uc720\uc81c\ub4e4\uc740 \uc544\uc8fc \uae30\ucd08\uc801\uc778 \ubb38\uc81c\uc774\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.23<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)=x^{3} +ax+2\\)\ub97c \\(x-1\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\uac00 \\(2\\)\uac00 \ub418\ub3c4\ub85d \\(a\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\ub098\uba38\uc9c0\uc815\ub9ac\uc5d0 \uc758\ud574 \ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \\(x-1\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub294 \\(P(1)\\)\uacfc \uac19\uc73c\ubbc0\ub85c<br \/>\n\\[<br \/>\nP(1)=1+a+2=2<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(a\\)\uc758 \uac12\uc740 \\(-1\\)\uc774\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.24<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)=x^{4}+ax^{2} -x+4\\)\ub97c \\(x+2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\uac00 \\(-2\\)\uac00 \ub418\ub3c4\ub85d \\(a\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.25<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \\(x+1\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub294 \\(1\\)\uc774\uace0, \\(x-2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ub098\uba38\uc9c0\ub294 \\(4\\)\uc774\ub2e4. \ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \\((x+1)(x-2)\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\uad6c\ud558\ub294 \ub098\uba38\uc9c0\ub97c \\(ax+b\\),\ubaab\uc744 \\(Q(x)\\)\ub77c\uace0 \ud558\uba74<span id='easy-footnote-16-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-16-4351' title=' \uc774\ucc28\uc2dd\uc73c\ub85c \ub098\ub204\uc5c8\uc73c\ub2c8 \ub098\uba38\uc9c0\ub294 \uc77c\ucc28\uc2dd \ub610\ub294 \uc0c1\uc218\uc774\ub2e4.'><sup>16<\/sup><\/a><\/span><br \/>\n\\[<br \/>\nP(x)=(x+1)(x-2)Q(x)+ax+b<br \/>\n\\]<br \/>\n\uc774\ub2e4. \uc774 \ud56d\ub4f1\uc2dd\uc758 \uc591\ubcc0\uc5d0 \\(x=-1, x=2\\)\ub97c \uac01\uac01 \ub300\uc785\ud558\uc5ec \ub098\uba38\uc9c0\uc815\ub9ac\uc640 \uc8fc\uc5b4\uc9c4 \uc870\uac74\uc73c\ub85c\ubd80\ud130 \ub450 \uac1c\uc758 \ub4f1\uc2dd<br \/>\n\\[<br \/>\nP(-1)=-a+b=1,\\quad P(2)=2a+b=4<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \uc774\ub85c\ubd80\ud130 \\(a=1, b=2\\)\ub97c \uc5bb\uace0 \ub530\ub77c\uc11c \ub530\ub77c\uc11c \uad6c\ud558\ub294 \ub098\uba38\uc9c0\ub294 \\(x+2\\)\uc774\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.26<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \\(x+2\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\ub294 \\(-7\\)\uc774\uace0, \\(x-3\\)\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\ub294 \\(3\\)\uc774\ub2e4. \ub2e4\ud56d\uc2dd \\(P(x)\\)\ub97c \\((x+2)(x-3)\\)\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c \ub098\uba38\uc9c0\ub97c \uad6c\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\ub098\uba38\uc9c0\uc815\ub9ac\uc5d0 \ub530\ub974\uba74 \ub2e4\ud56d\uc2dd \\(P(x)\\)\uac00 \uc77c\ucc28\uc2dd \\(x-a\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c8 \ub54c, \\(P(a)=0\\)\uc774\ub2e4. \uc5ed\uc73c\ub85c \\(P(a)=0\\)\uc774\uba74 \\(P(x)\\)\ub294 \uc77c\ucc28\uc2dd \\(x-a\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c4\ub2e4. \uc989 \ub2e4\uc74c\uc758 <span class=\"defined\">\uc778\uc218\uc815\ub9ac<\/span>\uac00 \uc131\ub9bd\ud568\uc744 \uc54c \uc218 \uc788\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Corollary 3.1.7 <\/span> (\uc778\uc218\uc815\ub9ac)<br \/>\n\ub2e4\ud56d\uc2dd \\(P(x)\\)\uac00 \uc77c\ucc28\uc2dd \\(x-a\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c0\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(P(a)=0\\)\uc778 \uac83\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.27<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(2x^{3} +ax^{2} +2x+b\\)\uac00 \\((x-1)(2x+1)\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c0\ub3c4\ub85d \\(a, b\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\\(P(x)=2x^{3}+ax^{2}+2x+b\\)\ub85c \ub450\uba74 \uc778\uc218\uc815\ub9ac\ub85c\ubd80\ud130<br \/>\n\\[<br \/>\nP(1)=0,\\quad P=\\left(-\\frac{1}{2}\\right) =0<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \uc989<br \/>\n\\[<br \/>\n2+a+2+b=0,\\quad -\\frac{1}{4}+\\frac{a}{4}-1+b=0<br \/>\n\\]<br \/>\n\uc774\uace0 \uc774\ub85c\ubd80\ud130 \\(a=-7, b=3\\)\uc784\uc744 \uc54c \uc218 \uc788\ub2e4.<br \/>\n<span class=\"qed\"><\/span> <\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.28<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(ax^{3} +bx^{2} -7x+6\\)\uc774 \\(x^{2} -3x+2\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c0\ub3c4\ub85d \\(a, b\\)\uc758 \uac12\uc744 \uc815\ud558\uc5ec\ub77c.\n<\/p>\n<p>\n\ub2e4\ud56d\uc2dd \\(P(x)\\)\uac00 \\(x-a\\)\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c4\ub2e4\ub294 \uac83\uc740<br \/>\n\\[<br \/>\nP(x)=(x-a)Q(x)<br \/>\n\\]<br \/>\n\uaf34\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4\ub294 \ub9d0\uc774\ub2e4. \uc774\uac83\uc740 \\(P(x)\\)\uac00 \\(x-a\\)\ub97c \uc778\uc218\ub85c \uac00\uc9c4\ub2e4\ub294 \ub73b\uc73c\ub85c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud560 \ub54c \uc778\uc218\uc815\ub9ac\uac00 \ub9e4\uc6b0  \uc720\uc6a9\ud558\uac8c \ud65c\uc6a9\ub420 \uc218 \uc788\uc74c\uc744 \ubcf4\uc5ec\uc900\ub2e4.\n<\/p>\n<h4> \uc778\uc218\ubd84\ud574 <\/h4>\n<p>\n\uc774\ubbf8 \uc911\ud559\uad50\uc5d0\uc11c \uc778\uc218\ubd84\ud574\ub97c \ud1b5\ud574 \uc774\ucc28\ubc29\uc815\uc2dd\uc758 \uadfc\uc744 \ucc3e\uc744 \uc218 \uc788\uc74c\uc744 \uc0b4\ud3b4\ubcf8 \ubc14 \uc788\ub2e4. \uc790\uc5f0\uc218\ub97c \uc18c\uc778\uc218\ubd84\ud574\ud558\uba74 \uadf8 \uc218\uc5d0 \ub300\ud55c \uc131\uc9c8\uc744 \ubcf4\ub2e4 \uba85\ud655\ud558\uac8c \ud30c\uc545\ud560 \uc218 \uc788\ub4ef\uc774 \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uba74 \uadf8 \ub2e4\ud56d\uc2dd\uc744 \uc798 \uc774\ud574\ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\ub294 \ubb38\uc81c\ub294 \uacb0\ucf54 \uc26c\uc6b4 \ubb38\uc81c\uac00 \uc544\ub2c8\ub2e4. \uc5ec\uae30\uc11c\ub294 \uc778\uc218\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574\ud558\ub294 \ubc29\ubc95, \uadf8\ub9ac\uace0 \uba87 \uac00\uc9c0 \uae30\ucd08\uc801\uc778 \uc778\uc218\ubd84\ud574 \uacf5\uc2dd\uc744 \ud65c\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574\ud558\ub294 \ubc29\ubc95\uc744 \uc54c\uc544\ubcf8\ub2e4.\n<\/p>\n<p>\n\uba3c\uc800 \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uae30 \uc704\ud574 \uadf8 \ub2e4\ud56d\uc2dd\uc774 \uc77c\ucc28\uc2dd\uc744 \uc778\uc218\ub85c \uac00\uc9c0\ub294\uc9c0\ub97c \uc778\uc218\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc0b4\ud3b4\ubcfc \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ub2e4\ud56d\uc2dd \\(P(x)=x^{3} -3x+2\\)\ub97c \uc778\uc218\ubd84\ud574\ud558\ub294 \uac83\uc744 \uc0dd\uac01\ud574\ubcf4\uc790. \ub2e4\ud56d\uc2dd \\(P(x)\\)\ub294 \ucd5c\uace0\ucc28\ud56d\uc758 \uacc4\uc218\uac00 \\(1\\)\uc774\ubbc0\ub85c \ub9cc\uc77c \uc774 \ub2e4\ud56d\uc2dd\uc774 \uc77c\ucc28\uc2dd\uc744 \uc778\uc218\ub85c \uac00\uc9c4\ub2e4\uba74<br \/>\n\\[<br \/>\nx^{3} -3x+2=(x-a)(x^{2} +bx+c)<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \uc77c\ucc28\uc2dd\uacfc \uc774\ucc28\uc2dd\uc758 \uacf1\uc73c\ub85c \uc778\uc218\ubd84\ud574\ub41c\ub2e4. \uc774 \ub4f1\uc2dd\uc740 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\ubbc0\ub85c \uc591\ubcc0\uc758 \uc0c1\uc218\ud56d\uc744 \ube44\uad50\ud558\uba74<br \/>\n\\[<br \/>\n-ac=2<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(a\\)\uac00 \uc815\uc218\ub77c\uba74 \uadf8 \uac12\uc740<span id='easy-footnote-17-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-17-4351' title=' \uc6b4\uc774 \uc88b\ub2e4\uba74 \uc815\uc218\uc77c \uac83\uc774\ub2e4.'><sup>17<\/sup><\/a><\/span><br \/>\n\\[<br \/>\n1,\\quad -1,\\quad 2,\\quad -2<br \/>\n\\]<br \/>\n\uac00\uc6b4\ub370 \ud558\ub098\uac00 \ub41c\ub2e4. \uc774 \uac12 \uac00\uc6b4\ub370 \\(1\\)\uc744 \\(P(x)\\)\uc5d0 \ub300\uc785\ud558\uc5ec \ubcf4\uba74<br \/>\n\\[<br \/>\nP(1)=0<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c \uc778\uc218\uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(P(x)\\)\ub294 \\(x-1\\)\uc744 \uc778\uc218\ub85c \uac00\uc9c4\ub2e4. \uc774\uc81c \uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uba74<br \/>\n<!-- \\begin{center}\n\\polyhornerscheme[x=1,resultbottomrule=true,resultleftrule=true]{x^{3} -3x+2}\n\\end{center} --><br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-309.png\" alt=\"\" width=\"190\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n\ub85c \uadf8 \ubaab\uc740 \\(x^{2} +x-2\\)\uc774\ubbc0\ub85c \\(x^{3} -3x+2\\)\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc778\uc218\ubd84\ud574\ub41c\ub2e4.\n<\/p>\n<p>\\begin{align*}<br \/>\nx^{3} -3x+2&#038;=(x-1)(x^{2} +x-2)\\\\<br \/>\n&#038; =(x-1)(x-1)(x+2) \\\\<br \/>\n&#038;=(x-1)^{2} (x+2)<br \/>\n\\end{align*}<\/p>\n<p>\n\uc774\ucc98\ub7fc \uc0bc\ucc28 \uc774\uc0c1\uc758 \ub2e4\ud56d\uc2dd\uc5d0\uc11c \uc778\uc218\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc77c\ucc28\uc2dd\uc758 \uc778\uc218\ub97c \ucc3e\uc73c\uba74 \uc870\ub9bd\uc81c\ubc95\uc744 \ud65c\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574\ub97c \ud560 \uc218 \uc788\ub2e4.<span id='easy-footnote-18-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-18-4351' title=' \ubb3c\ub860 \ucc28\uc218\uac00 3, 4, \\(n\\)\uc778 \ub2e4\ud56d\uc2dd\uc744 \uac01\uac01 \uc0bc\ucc28, \uc0ac\ucc28, \\(n\\)\ucc28 \ub2e4\ud56d\uc2dd\uc774\ub77c\uace0 \ud55c\ub2e4. '><sup>18<\/sup><\/a><\/span>\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.29<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c. <\/p>\n<ol class=\"parenthesis\">\n<li> \\(x^{3} -1\\)  <\/li>\n<li> \\(x^{3} -x^{2} -5x-3\\)  <\/li>\n<li> \\(x^{4} -2x^{3} +x-2\\)  <\/li>\n<li> \\(x^{4} -3x^{3} +3x^{2} -3x+2\\) <\/li>\n<\/ol>\n<p>\n\uc774\ubc88\uc5d0\ub294 \ucd5c\uace0\ucc28\ud56d\uc758 \uacc4\uc218\uac00 \\(1\\)\uc774 \uc544\ub2cc \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud560 \ub54c \uc778\uc218\uc815\ub9ac\uc640 \uc870\ub9bd\uc81c\ubc95\uc744 \uc5b4\ub5bb\uac8c \uc774\uc6a9\ud558\ub294\uc9c0 \uc54c\uc544\ubcf4\uc790.\n<\/p>\n<p>\n\uc608\ub97c \ub4e4\uc5b4 \ub2e4\ud56d\uc2dd \\(P(x)=2x^{3} +x^{2} +x-1\\)\uc758 \uc778\uc218\ubd84\ud574\ub97c \uc2dc\ub3c4\ud574\ubcf4\uc790. \ub9cc\uc77c \ub2e4\ud56d\uc2dd \\(P(x)\\)\uac00 \uc778\uc218\ubd84\ud574\ub41c\ub2e4\uba74<br \/>\n\\[<br \/>\n2x^{3} +x^{2} +x-1=(ax-b)(cx^{2} +dx+e)<br \/>\n\\]<br \/>\n\uaf34\uc774\ub2e4. \uc774 \ub4f1\uc2dd\uc740 \\(x\\)\uc5d0 \ub300\ud55c \ud56d\ub4f1\uc2dd\uc774\ubbc0\ub85c \\(x^{3}\\)\uc758 \uacc4\uc218\uc640 \uc0c1\uc218\ud56d\uc744 \ube44\uad50\ud588\uc744 \ub54c<br \/>\n\\[<br \/>\n ac=2,\\quad be=1<br \/>\n \\]<br \/>\n\uc774 \uc131\ub9bd\ud574\uc57c\ub9cc \ud568\uc744 \uc54c \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \ub9cc\uc77c \\(a\\)\uc640 \\(b\\)\uac00 \uc815\uc218\ub77c\uba74, \\(a\\)\ub294 \\(2\\)\uc758 \uc57d\uc218\uc774\uace0 \\(b\\)\ub294 \\(1\\)\uc758 \uc57d\uc218\uc784\uc744 \uc54c \uc218 \uc788\uc73c\uba70 \uacb0\uad6d \\(\\frac{b}{a}\\)\uc758 \uac12\uc740 <span id='easy-footnote-19-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-19-4351' title=' \uc6b4\uc774 \uc88b\ub2e4\uba74 \uc815\uc218\uc77c \uac83\uc774\ub2e4(\ud56d\uc0c1 \uc6b4\uc774 \uc88b\uc740 \ub290\ub08c?).'><sup>19<\/sup><\/a><\/span><br \/>\n\\[<br \/>\n1,\\quad -1,\\quad \\frac{1}{2} ,\\quad -\\frac{1}{2}<br \/>\n\\]<br \/>\n\uc911 \ud558\ub098\ub77c\ub294 \uac83\uc744 \uc54c \uc218 \uc788\ub2e4. \uc989 \uc774 \uac12\ub4e4\uc774 \ubc14\ub85c \uc778\uc218\uc815\ub9ac\ub97c \ud1b5\ud574 \\(P(x)\\)\uc758 \uc77c\ucc28\uc778\uc218\ub97c \ucc3e\uc744 \ub54c \uc0ac\uc6a9\ud558\ub294 \ubc29\uc815\uc2dd \\(P(x)=0\\)\uc758 \uadfc\uc758 \ud6c4\ubcf4\uc778 \uac83\uc774\ub2e4. \uc774 \uac12\ub4e4\uc744 \\(P(x)\\)\uc5d0 \ucc28\ub840\ub85c \ub300\uc785\ud558\uc5ec \ubcf4\uba74 \\(P\\left(\\frac{1}{2}\\right)=0\\)\uc784\uc744 \ud655\uc778\ud560 \uc218 \uc788\uace0 \uc778\uc218\uc815\ub9ac\ub85c\ubd80\ud130 \\(P(x)\\)\ub294 \\(x-\\frac{1}{2}\\)\uc744 \uc778\uc218\ub85c \uac00\uc9d0\uc744 \uc54c \uc218 \uc788\ub2e4. \uc774\uc81c \uc870\ub9bd\uc81c\ubc95\uc744 \uc774\uc6a9\ud558\uba74<br \/>\n<!--\\begin{center}\n\\polyhornerscheme[x=1\/2,resultbottomrule=true,resultleftrule=true]{2x^{3} +x^{2} +x-1}\n\\end{center} --><br \/>\n<img decoding=\"async\" src=\"https:\/\/coslimites.com\/wp-content\/uploads\/2020\/03\/fig-310.png\" alt=\"\" width=\"170\" height=\"\" class=\"aligncenter size-full wp-image-1936\" \/><br \/>\n\ub85c \\(P(x)\\)\ub97c \\(x-\\frac{1}{2}\\)\ub85c \ub098\ub204\uc5c8\uc744 \ub54c\uc758 \ubaab\uc740 \\(2x^{2}+2x+2\\)\uc784\uc744 \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c \uad6c\ud558\ub294 \uc2dd\uc740<br \/>\n\\[<br \/>\n2x^{3} +x^{2} +x-1=\\left(x-\\frac{1}{2}\\right)\\left(2x^{2} +2x+2\\right)=(2x-1)\\left(x^{2} +x+1\\right)<br \/>\n\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<p>\n\uc704\uc758 \uc778\uc218\ubd84\ud574 \uacfc\uc815\uc5d0\uc11c \uac00\uc7a5 \uc911\uc694\ud55c \uc7a5\uba74\uc740 \uc778\uc218\uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\ub294 \uc7a5\uba74\uc774\ub2e4. \uc774\ub294 \uace7 \uc8fc\uc5b4\uc9c4 \ub2e4\ud56d\uc2dd\uc758 \ud55c \uadfc\uc744 \ucc3e\uc544\ub0b4\ub294 \uc7a5\uba74\uc774\ub77c \ud560 \uc218 \uc788\ub294\ub370 \ubb34\uc218\ud788 \ub9ce\uc740 \ud6c4\ubcf4\ub4e4\uc744 \ub300\ucc45\uc5c6\uc774 \ub300\uc785\ud558\ub294 \uac83\uc774 \uc544\ub2c8\ub77c<span id='easy-footnote-20-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-20-4351' title='&amp;#8216;\ub2e4\ud56d\uc2dd \\(P(x)\\)\uc758 \uadfc&amp;#8217;\uc774\ub780  \ubc29\uc815\uc2dd \\(P(x)=0\\)\uc758 \uadfc\uc774\ub2e4.'><sup>20<\/sup><\/a><\/span><br \/>\n\\[<br \/>\n\\pm\\frac{(\\text{\uc0c1\uc218\ud56d\uc758 \uc57d\uc218})}{(\\text{\ucd5c\uace0\ucc28\ud56d \uacc4\uc218\uc758 \uc57d\uc218})}<br \/>\n\\]<br \/>\n\ub97c \uc6b0\uc120\uc801\uc73c\ub85c \ub300\uc785\ud558\uc5ec \uadf8 \uadfc\uc744 \ucc3e\uc544\ub0b4\ub294 \uac83\uc774 \uadf8 \uacfc\uc815\uc758 \ud575\uc2ec\uc801\uc778  \ubd80\ubd84\uc774\ub77c \ud560 \uc218 \uc788\uaca0\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.30<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(2x^{3} -x^{2} +x+1\\) <\/li>\n<li> \\(3x^{3} +2x^{2} -4x+1\\) <\/li>\n<\/ol>\n<p>\n\uc774\uc81c \uba87 \uac00\uc9c0 \uae30\ucd08\uc801\uc778 \uacf5\uc2dd\ub4e4\uc744 \ud65c\uc6a9\ud55c \uc778\uc218\ubd84\ud574\ub97c \uc54c\uc544\ubcf4\uc790. \uc778\uc218\ubd84\ud574\ub418\ub294 \uc774\ucc28\uc2dd\uc774\ub098 \uc0bc\ucc28\uc2dd\uc740 \ubc18\ub4dc\uc2dc \uc77c\ucc28\uc2dd\uc744 \uc778\uc218\ub85c \uac00\uc9c4\ub2e4. <span id='easy-footnote-21-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-21-4351' title=' \uc5b4\ub5a4 \ub2e4\ud56d\uc2dd\uc774 \uc778\uc218\ubd84\ud574\uac00 \ub418\ub294\uc9c0, \ub418\uc9c0 \uc54a\ub294\uc9c0\ub294 \uc778\uc218\ubd84\ud574\ub97c &amp;#8216;\uc5b4\ub290 \ub3d9\ub124&amp;#8217;\uc5d0\uc11c \ud558\ub294\uac00\uc5d0 \ub2ec\ub824\uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uc774\ucc28\uc2dd \\(x^{2}+1\\)\uc740 &amp;#8216;\uc2e4\uc218\uacc4\uc218 \ub2e4\ud56d\uc2dd \ub3d9\ub124&amp;#8217;\uc5d0\uc11c\ub294 \ub354 \ub0ae\uc740 \ucc28\uc218\uc758 \ub2e4\ud56d\uc2dd\ub4e4\ub85c \uc778\uc218\ubd84\ud574\ud560 \uc218 \uc5c6\ub2e4. \uadf8\ub7ec\ub098 \uc774 \ub2e4\ud56d\uc2dd\uc740 \ubb3c\ub860 &amp;#8216;\ubcf5\uc18c\uacc4\uc218 \ub2e4\ud56d\uc2dd  \ub3d9\ub124&amp;#8217;\uc5d0\uc11c \\[x^{2}+1=(x+i)(x-i)\\]\ub85c \uc778\uc218\ubd84\ud574\ub41c\ub2e4. \ub530\ub77c\uc11c \uc778\uc218\ubd84\ud574\ub97c &amp;#8216;\uc5b4\ub290 \ub3d9\ub124&amp;#8217;\uc5d0\uc11c \ud558\ub290\ub0d0\ub294 \uc0ac\uc2e4 \uc544\uc8fc \uc911\uc694\ud55c \ubb38\uc81c\ub77c \ud560 \uc218 \uc788\ub2e4.  &lt;\/p&gt;\n&lt;p&gt;\uc55e\uc73c\ub85c \ubcc4\ub2e4\ub978 \uc5b8\uae09\uc774 \uc5c6\uc774 \uc5b4\ub5a4 \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\ub77c\uace0 \ud558\uba74 \uc6b0\uc120\uc801\uc73c\ub85c \uc720\ub9ac\uc218 \uacc4\uc218 \ub2e4\ud56d\uc2dd \ubc94\uc704\uc5d0\uc11c \ud558\ub294 \uac83\uc744 \uc0dd\uac01\ud55c\ub2e4. \uadf8\ub7ec\ub098 \uc720\ub9ac\uacc4\uc218 \ubc94\uc704\uc5d0\uc11c \uc778\uc218\ubd84\ud574\ub97c \ud55c \ud6c4\uc5d0\ub3c4 \uc8fc\uc5b4\uc9c4 \ub2e4\ud56d\uc2dd\uc774 \uc2e4\uacc4\uc218 \ubc94\uc704\uc5d0\uc11c\ub294 \uc5b4\ub5bb\uac8c \uc778\uc218\ubd84\ud574\ub418\ub294\uc9c0, \ubcf5\uc18c\uacc4\uc218 \ubc94\uc704\uc5d0\uc11c\ub294 \uc5b4\ub5bb\uac8c \uc778\uc218\ubd84\ud574\ub418\ub294\uc9c0  \uc2ac\uca4d \uc0dd\uac01\ud574\ubcf4\ub294 \uac83\ub3c4 \ub098\uc058\uc9c0 \uc54a\ub2e4.&lt;br \/&gt;\n '><sup>21<\/sup><\/a><\/span><br \/>\n\uadf8\ub7ec\ub098 \uc0ac\ucc28\uc2dd\uc740 \uc778\uc218\ubd84\ud574\ub41c\ub2e4\uace0 \ud574\uc11c \ubc18\ub4dc\uc2dc \uc77c\ucc28\uc2dd\uc744 \uc778\uc218\ub85c \uac00\uc9c0\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ub450 \ud56d\ub4f1\uc2dd<br \/>\n\\begin{align*}<br \/>\n&#038;x^{4} +4x^{2} +3=(x^{2} +1)(x^{2} +3), \\\\<br \/>\n&#038;x^{4} +x^{2} +1=(x^{2} +x+1)(x^{2} -x+1)<br \/>\n\\end{align*}<br \/>\n\uc758 \uacbd\uc6b0\ub97c \uc0b4\ud3b4\ubcf4\uc790. \uc774 \uc2dd\uc758 \uc88c\ubcc0\uc5d0 \uc788\ub294 \uc0ac\ucc28\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud55c \uac83\uc774 \uc6b0\ubcc0\uc778\ub370, \uc6b0\ubcc0\uc758 \uc774\ucc28\uc2dd\ub4e4\uc740 \ub354 \uc774\uc0c1 \uc778\uc218\ubd84\ud574\ub418\uc9c0 \uc54a\ub294\ub2e4. \uc774\ub294 \uc88c\ubcc0\uc758 \uc0ac\ucc28\uc2dd\ub4e4\uc740 \uc778\uc218\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574\ud560 \uc218 \uc5c6\ub2e4\ub294 \uac83\uc744 \uc54c \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\uc774\uc640 \uac19\uc774 \uc778\uc218\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574\ud560 \uc218 \uc5c6\ub294 \uc0ac\ucc28\uc2dd \uac00\uc6b4\ub370 \uba3c\uc800 \uc0ac\ucc28\ud56d, \uc774\ucc28\ud56d, \uc0c1\uc218\ud56d\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \\(ax^{4} +bx^{2} +c\\)\uaf34\uc758 \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec \ubcf4\uc790.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.31<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(x^{4} +4x^{2} +3\\)\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\\(x^{2} =X\\)\ub85c \ub193\uc73c\uba74 \uc8fc\uc5b4\uc9c4 \ub2e4\ud56d\uc2dd\uc740<br \/>\n\\begin{align*}<br \/>\nx^{4} +4x^{2} +3&#038;=X^{2} +4X+3\\\\<br \/>\n&#038; =(X+1)(X+3)<br \/>\n\\end{align*}<br \/>\n\ub85c \uc4f8 \uc218 \uc788\ub2e4.<span id='easy-footnote-22-4351' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/sasamath.com\/blog\/articles\/sasa-textbook-math1-04\/#easy-footnote-bottom-22-4351' title=' \\(x^{2} =X\\)\ub85c \uce58\ud658\ud588\uc744 \ub54c, \\(X\\)\uc5d0 \ub300\ud55c \uc774\ucc28\uc2dd\uc774 \uc778\uc218\ubd84\ud574\ub418\ub294 \uacbd\uc6b0\uc774\ub2e4.'><sup>22<\/sup><\/a><\/span>  \uc5ec\uae30\uc11c \\(X\\)\uc5d0 \\(x^{2}\\)\uc744 \ub300\uc785\ud558\uc5ec<br \/>\n\\[<br \/>\nx^{4} +4x^{2} +3=(x^{2} +1)(x^{2} +3)<br \/>\n\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4.<br \/>\n<span class=\"qed\"><\/span> <\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.32<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(x^{4} +5x^{2} +4\\) <\/li>\n<li> \\(2x^{4} +7x^{2} +6\\)  <\/li>\n<li> \\(5x^{4} +16x^{2} +3\\)  <\/li>\n<li> \\(2x^{4} +3x^{2} +1\\)  <\/li>\n<\/ol>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.33<\/span><br \/>\n\ub2e4\ud56d\uc2dd \\(x^{4} +x^{2} +1\\)\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.\n<\/p>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><br \/>\n\\(x^{2} =X\\)\ub85c \uce58\ud658\ud558\ub294 \uac83\uc744 \uc0dd\uac01\ud574\ubcf4\ub2c8, \uce58\ud658\ud558\uc5ec \uc5bb\uc740 \uc774\ucc28\uc2dd\uc774 \uc778\uc218\ubd84\ud574\ub418\uc9c0 \uc54a\ub294\ub2e4\ub294 \uac83\uc744 \ubc14\ub85c \uc54c \uc218 \uc788\ub2e4. \uc774 \uacbd\uc6b0\uc5d0\ub294 \uc774\ucc28\ud56d\uc744 \uc801\uc808\ud558\uac8c \ub354\ud558\uace0 \ube7c\uc11c \\(A^{2}-B^{2}\\) \uaf34\ub85c \ubcc0\ud615\ud55c\ub2e4.<br \/>\n \uc774 \uc608\uc81c\uc758 \uacbd\uc6b0\uc5d0\ub294 \\(x^{2}\\)\uc744 \ub354\ud558\uace0 \ube7c\uc11c \\(A^{2}-B^{2}\\) \uaf34\ub85c \uc2dd\uc744 \ubcc0\ud615\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc778\uc218\ubd84\ud574\ud55c\ub2e4.<br \/>\n \\begin{align*}<br \/>\n x^{4} +x^{2} +1&#038;= x^{4} +2x^{2} +1-x^{2}  \\\\<br \/>\n&#038; =(x^{4} +2x^{2} +1)-x^{2} \\\\<br \/>\n&#038; =(x^{2} +1)^{2} -x^{2} \\\\<br \/>\n&#038; =(x^{2} +x+1)(x^{2} -x+1)<br \/>\n\\end{align*}<br \/>\n<span class=\"qed\"><\/span><\/p>\n<p><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.34<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c. <\/p>\n<ol class=\"parenthesis\">\n<li> \\(x^{4} +3x^{2} +4\\)  <\/li>\n<li> \\(x^{4} -6x^{2} +1\\)  <\/li>\n<li> \\(x^{4} +2x^{2} +9\\)  <\/li>\n<li> \\(x^{4} -9x^{2} +16\\)  <\/li>\n<\/ol>\n<p>\n\ub450 \uac1c \uc774\uc0c1\uc758 \ubb38\uc790\ub97c \ud3ec\ud568\ud558\ub294 \ub2e4\ud56d\uc2dd\uc740 \ud55c \ubb38\uc790\uc5d0 \ub300\ud558\uc5ec \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uc5ec \uc778\uc218\ubd84\ud574\ud558\ub294 \uac83\uc774 \uc694\ub839\uc774\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc608\uc81c 3.35<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(ab+bc-cd-da\\) <\/li>\n<li> \\(2x^{2} +5xy+3y^{2} +3x+5y-2\\) <\/li>\n<\/ol>\n<p class=\"proofbegin\">\n\t<span class=\"proof\">Sol.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li> \\(a\\)\uc5d0 \ub300\ud558\uc5ec \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc778\uc218\ubd84\ud574\ud55c\ub2e4.<br \/>\n\\begin{align*}<br \/>\n ab+bc-cd-da&#038;=a(b-d)+bc-cd \\\\<br \/>\n&#038; =a(b-d)+c(b-d)\\\\<br \/>\n &#038; =(a+c)(b-d)<br \/>\n \\end{align*} <\/li>\n<li> \\(x\\)\uc5d0 \ub300\ud558\uc5ec \ub0b4\ub9bc\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc778\uc218\ubd84\ud574\ud55c\ub2e4.<br \/>\n \\begin{align*}<br \/>\n&#038; 2x^{2} +5xy+3y^{2} +3x+5y-2\\\\<br \/>\n &#038;\\phantom{MMM} =2x^{2} +(5y+3)x+(3y^{2} +5y-2) \\\\<br \/>\n&#038;\\phantom{MMM} =2x^{2} +(5y+3)x+(y+2)(3y-1) \\\\<br \/>\n&#038;\\phantom{MMM} =(x+y+2)(2x+3y-1)<br \/>\n\\end{align*} <\/li>\n<\/ol>\n<p><span class=\"qed\"><\/span><\/p>\n<p><\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.36<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(ac+2bc-2bd-ad\\)  <\/li>\n<li> \\(3x^{2} -2xy-y^{2} -5x+y+2\\)  <\/li>\n<li> \\(a^{2} +b^{2} +ac-bc-2ab\\)  <\/li>\n<li> \\(x^{2} +3xy+2y^{2} -x-3y-2\\)  <\/li>\n<\/ol>\n<p>\n\uc778\uc218\ubd84\ud574\ub294 \ubb3c\ub860 \ub2e4\ud56d\uc2dd\uc758 \uc804\uac1c \uacfc\uc815\uc744 \uc5ed\uc73c\ub85c \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \ub2e4\uc74c\uc740 \uacf1\uc148 \uacf5\uc2dd\uc5d0\uc11c \uc88c\ubcc0\uacfc \uc6b0\ubcc0\uc744 \ubc14\uafb8\uc5b4 \uc368\uc11c \uc5bb\uc740 \uacf5\uc2dd\uc774\ub2e4.\n<\/p>\n<div class=\"theorem\">\n<p>\n\t\t<span class=\"theorem\"> Theorem 3.1.8 <\/span> (\uc778\uc218\ubd84\ud574 \uacf5\uc2dd)<\/p>\n<ol class=\"parenthesis-roman\">\n<li> \\(a^{2} +b^{2} +c^{2} +2ab+2bc+2ca=(a+b+c)^{2}\\) <\/li>\n<li> \\( a^{3} +3a^{2} b+3ab^{2} +b^{3} =(a+b)^{3} ,\\) <br \/>\n\t\t\\( a^{3} -3a^{2} b+3ab^{2} -b^{3} =(a-b)^{3} \\) <\/li>\n<li> \\( a^{3} +b^{3} =(a+b)(a^{2} -ab+b^{2} ) ,\\) <br \/>\n\t\t \\( a^{3} -b^{3} =(a-b)(a^{2} +ab+b^{2} ) \\) <\/li>\n<\/ol>\n<\/div>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.37<\/span><br \/>\n\uc778\uc218\ubd84\ud574 \uacf5\uc2dd\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(x^{3} -8\\)   <\/li>\n<li> \\(x^{3} +6x^{2} +12x+8\\) <\/li>\n<li> \\( 27x^{3} +1\\)  <\/li>\n<li>  \\(x^{3} -6x^{2} +12x-8\\) <\/li>\n<li> \\(8x^{3} -y^{3} \\)  <\/li>\n<li> \\( a^{2} +b^{2} +c^{2} -2ab+2bc-2ca\\) <\/li>\n<\/ol>\n<p>\n\ubb3c\ub860 \ub2e4\ud56d\uc2dd\uc740 \uc5ec\ub7ec \uac00\uc9c0 \ubc29\ubc95\uc73c\ub85c \uc778\uc218\ubd84\ud574\ud560 \uc218 \uc788\ub2e4. \uc2e4\uc81c\ub85c \uc704 \uc778\uc218\ubd84\ud574 \uacf5\uc2dd\ub4e4\uc744 \uc774\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574 \ud560 \uc218 \uc788\ub294 \ub2e4\ud56d\uc2dd\uc740 \ubaa8\ub450 \uc778\uc218\uc815\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc778\uc218\ubd84\ud574\ud560 \uc218 \uc788\ub2e4.\n<\/p>\n<p>\n\t\t<span class=\"definition\"> \uc720\uc81c 3.38<\/span><br \/>\n\ub2e4\uc74c \ub2e4\ud56d\uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uc5ec\ub77c.<\/p>\n<ol class=\"parenthesis\">\n<li> \\(x^{4} -1\\)   <\/li>\n<li> \\(x^{3} -8y^{3}\\) <\/li>\n<li> \\(x^{4} -4\\)  <\/li>\n<li>  \\(x^{3} -3x^{2} y+3xy^{2} -y^{3}\\) <\/li>\n<\/ol>\n<hr>\n","protected":false},"excerpt":{"rendered":"<p>\uc81c3\uc7a5 \ubb38\uc790\uc640 \uc2dd 3.1 \ub2e4\ud56d\uc2dd \ub2e4\ud56d\uc2dd\uc758 \uad6c\uc870 \ubb38\uc790 \ub610\ub294 \uc218\ub4e4\uc758 \uacf1\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc2dd\uc744 \ud56d\uc774\ub77c \ud558\uace0, \ud56d \ub610\ub294 \ud56d\ub4e4\uc758 \ud569\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc2dd\uc744 \ub2e4\ud56d\uc2dd(polynomial)\uc774\ub77c\uace0 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \\( \\pi,\\, x,\\, 3z+1,\\, -x+2x^{2020}+2, \\, -xy^{2}+x^{2}+a^{4}y^{2}+x \\) \ub294 \ubaa8\ub450 \ub2e4\ud56d\uc2dd\uc774\ub2e4. \ub2e4\ud56d\uc2dd\uc740 \ub3d9\ub958\ud56d\ub07c\ub9ac \ubaa8\uc544\uc11c \uc815\ub9ac\ud558\uc5ec \uac04\ub2e8\ud788 \ub098\ud0c0\ub0b8\ub2e4. \uadf8\ub9ac\uace0 \ucc28\uc218\uac00 \ub192\uc740 \ud56d\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ub098\uc5f4\ud558\ub294 \ub0b4\ub9bc\ucc28\uc21c \ud639\uc740 \ucc28\uc218\uac00 \ub0ae\uc740 \ud56d\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ub098\uc5f4\ud558\ub294 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub9ac\ud558\uba74 \ubcf4\uae30 \uc88b\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ub2e4\ud56d\uc2dd \\(-x+2x^{2020}+2\\)\ub97c 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