{"id":314,"date":"2023-07-06T08:26:38","date_gmt":"2023-07-06T08:26:38","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%9b%a0%e5%ad%90%e5%ae%9a%e7%90%86\/"},"modified":"2023-07-06T08:26:38","modified_gmt":"2023-07-06T08:26:38","slug":"%e5%9b%a0%e5%ad%90%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%9b%a0%e5%ad%90%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u56e0\u5b50\u5b9a\u7406"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u56e0\u5b50\u5b9a\u7406\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c55\u793a\u4e86\u56e0\u5f0f\u5b9a\u7406\u7684\u7528\u9014\uff1a\u591a\u9879\u5f0f\u7684\u6574\u9664\u6027\u3001\u6c42\u6839\u3001\u56e0\u5f0f\u5206\u89e3\u591a\u9879\u5f0f\u7b49\u3002\u6700\u540e\uff0c\u60a8\u5c06\u80fd\u591f\u9010\u6b65\u7ec3\u4e60\u56e0\u5b50\u5b9a\u7406\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-teorema-del-factor\"><\/span>\u4ec0\u4e48\u662f\u56e0\u6570\u5b9a\u7406\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u56e0\u5b50\u5b9a\u7406<\/strong>\u8868\u793a\uff0c\u5f53\u4e14\u4ec5\u5f53 P(a)=0 \u65f6\uff0c\u591a\u9879\u5f0f P(x) \u624d\u80fd\u88ab\u53e6\u4e00\u4e2a (xa) \u5f62\u5f0f\u7684\u591a\u9879\u5f0f\u6574\u9664\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/theoreme-des-facteurs.jpg\" alt=\"\u56e0\u5b50\u5b9a\u7406\" class=\"wp-image-2179\" width=\"247\" height=\"247\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u540c\u6837\uff0c\u6839\u636e\u56e0\u5b50\u5b9a\u7406\uff0c\u5982\u679c\u591a\u9879\u5f0f P(x) \u53ef\u88ab (x\u2212a) \u6574\u9664\uff0c\u5219\u610f\u5473\u7740\u503c a \u662f\u591a\u9879\u5f0f P( x) \u7684\u6839\uff08\u6216\u96f6\uff09 \uff09\u3002<\/p>\n<p>\u4e00\u4e2a\u591a\u9879\u5f0f\u53ef\u88ab\u53e6\u4e00\u4e2a\u591a\u9879\u5f0f\u6574\u9664\u610f\u5473\u7740\u4e24\u4e2a\u591a\u9879\u5f0f\u76f8\u9664\u7684\u4f59\u6570\uff08\u6216\u4f59\u6570\uff09\u7b49\u4e8e\u96f6\u3002\u5982\u679c\u60a8\u4e0d\u5b8c\u5168\u8bb0\u4f4f\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5728\u4e0b\u9762\u7684\u94fe\u63a5\u4e2d\u60a8\u53ef\u4ee5\u770b\u5230<a href=\"https:\/\/mathority.org\/cn\/\u591a\u9879\u5f0f\u9664\u6cd5-\u4f8b\u5b50-\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60-\u9664\u6cd5\/\"><strong><span style=\"text-decoration: underline;\">\u591a\u9879\u5f0f\u9664\u6cd5\u7684\u793a\u4f8b<\/span><\/strong><\/a>\uff0c\u5728\u90a3\u91cc\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u5982\u4f55\u5212\u5206\u591a\u9879\u5f0f\u7684\u8bf4\u660e\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-del-teorema-del-factor\"><\/span>\u56e0\u5b50\u5b9a\u7406\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u56e0\u5b50\u5b9a\u7406\u7684\u6570\u5b66\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u51e0\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5b83\u662f\u5982\u4f55\u5e94\u7528\u7684\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<p>\u56e0\u5b50\u5b9a\u7406\u7684\u4e00\u4e2a\u5e94\u7528\u662f\u627e\u51fa\u7ed9\u5b9a\u7684\u591a\u9879\u5f0f\u662f\u5426\u53ef\u88ab<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u4e8c\u9879\u5f0f\/\">\u4e8c\u9879\u5f0f<\/a><\/span><\/strong>\u6574\u9664\u3002\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u5982\u4f55\u4f7f\u7528\u56e0\u5b50\u5b9a\u7406\u6765\u5b8c\u6210\u6b64\u64cd\u4f5c\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u786e\u5b9a\u591a\u9879\u5f0f P(x) \u662f\u5426\u80fd\u88ab\u4e8c\u9879\u5f0f Q(x) \u6574\u9664\uff0c\u4e24\u8005\u5747\u4e3a\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67a5b0b8df744da98b4d71433f73c9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^2-4x+3 \\qquad \\qquad Q(x)=x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"323\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u9664\u6570\u591a\u9879\u5f0f Q(x) \u662f (xa) \u7c7b\u578b\u7684\u591a\u9879\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u56e0\u5b50\u5b9a\u7406\u6765\u89e3\u51b3\u8be5\u95ee\u9898\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u68c0\u67e5 P(x) \u662f\u5426\u53ef\u4ee5\u9664\u4ee5 Q(x)\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97 x=1 \u65f6\u591a\u9879\u5f0f P(x) \u7684\u6570\u503c\uff0c\u56e0\u4e3a 1 \u662f\u9664\u6cd5\u591a\u9879\u5f0f\u7684\u72ec\u7acb\u9879\uff0c\u5176\u7b26\u53f7\u53d1\u751f\u4e86\u53d8\u5316:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-00216efc4a2e53b0b38de1175e73a5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(1) &amp; =1^2-4\\cdot 1+3 \\\\[2ex] &amp; = 1-4+3 \\\\[2ex] &amp; = 0 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> x = 1 \u65f6\u591a\u9879\u5f0f P(x) \u7684\u6570\u503c\u4e3a\u96f6\uff0c\u56e0\u6b64\u6839\u636e\u56e0\u5b50\u5b9a\u7406 P(x) \u53ef\u4ee5\u88ab Q(x) \u6574\u9664\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e24\u8005\u76f8\u9664\u7684\u4f59\u6570\u5c06\u4e3a\u7a7a\u3002<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06 2 \u4e2a\u591a\u9879\u5f0f\u9664\u4ee5<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u89c4\u5219\u5df2\u89e3\u51b3\u793a\u4f8b\u9c81\u83f2\u5c3c\u7ec3\u4e60\/\">\u9c81\u83f2\u5c3c\u5b9a\u7406<\/a><\/span><\/strong>\u6765\u9a8c\u8bc1\u662f\u5426\u6ee1\u8db3\u6574\u9664\u6761\u4ef6\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/theoreme-factoriel-exercices-resolus-pdf.jpg\" alt=\"\u56e0\u5b50\u5b9a\u7406\u6c42\u89e3\u7ec3\u4e60 pdf \u5728\u7ebf\" class=\"wp-image-2189\" width=\"172\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u5728\u672c\u4f8b\u4e2d\u770b\u5230\u7684\uff0c\u56e0\u5b50\u5b9a\u7406\u662f\u4f59\u6570\uff08\u6216\u4f59\u6570\uff09\u5b9a\u7406\u7684\u7279\u4f8b\u3002\u6211\u7ed9\u60a8\u7559\u4e0b\u8fd9\u7bc7\u6587\u7ae0\uff0c\u5b83\u89e3\u91ca\u4e86<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u4f59\u6570\u5b9a\u7406\u793a\u4f8b\u548c\u4e60\u9898\u5df2\u89e3\u51b3\/\">\u4f59\u6570\u5b9a\u7406<\/a><\/span><\/strong>\u662f\u4ec0\u4e48\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u7528\u5b83\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002\u800c\u4e14\uff0c\u66f4\u91cd\u8981\u7684\u662f\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f59\u6570\u5b9a\u7406\u548c\u56e0\u5b50\u5b9a\u7406\u4e4b\u95f4\u7684\u533a\u522b\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b2<\/h3>\n<p>\u56e0\u5b50\u5b9a\u7406\u4e5f\u53ef\u7528\u4e8e\u67e5\u627e\u591a\u9879\u5f0f\u7684\u6839\uff08\u6216\u96f6\u70b9\uff09\u3002\u4f46\u662f\uff0c\u663e\u7136\uff0c\u8981\u7406\u89e3\u6b64\u7c7b\u95ee\u9898\uff0c\u60a8\u9700\u8981\u77e5\u9053<a href=\"https:\/\/mathority.org\/cn\/\u591a\u9879\u5f0f\u7684\u6839\/\"><strong><span style=\"text-decoration: underline;\">\u591a\u9879\u5f0f\u7684\u6839\u662f\u4ec0\u4e48<\/span><\/strong><\/a>\u3002\u5982\u679c\u4f60\u8fd8\u662f\u4e0d\u660e\u767d\u8fd9\u4e2a\u6982\u5ff5\uff0c\u4f60\u53ef\u4ee5\u770b\u4e00\u4e0b\u94fe\u63a5\u9875\u9762\uff0c\u91cc\u9762\u6709\u8be6\u7ec6\u7684\u89e3\u91ca\u3002<\/p>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u5e94\u7528\u56e0\u5b50\u5b9a\u7406\u6765\u6c42\u591a\u9879\u5f0f\u7684\u6839\uff1a<\/p>\n<ul>\n<li>\u7ed9\u5b9a\u591a\u9879\u5f0f P(x)\uff0c\u8ba1\u7b97\u5176\u6839\u4e4b\u4e00\u662f\u5426\u4e3a x=2\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3d4052b7ff040dd41473d225569289b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3-3x^2+5x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5e94\u7528\u56e0\u5b50\u5b9a\u7406\uff0c\u5982\u679c x=2 \u7684 P(x) \u6570\u503c\u4e3a\u96f6\uff0c\u5219 x=2 \u9879\u5c06\u4ec5\u662f\u591a\u9879\u5f0f P(x) \u7684\u6839\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u627e\u5230\u8fd9\u4e2a\u6570\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82d50f0361613cb6c540051f8da4bc20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(2) &amp; =2^3-3\\cdot 2^2+5\\cdot 2-6 \\\\[2ex] &amp; = 8-3\\cdot 4 +5\\cdot 2 -6\\\\[2ex] &amp; = 8-12+10-6 \\\\[2ex] &amp; = 0\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"219\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u591a\u9879\u5f0f P(x) \u7684\u6570\u503c\u5728 x=2 \u65f6\u6d88\u5931\uff0c\u56e0\u6b64\u501f\u52a9\u56e0\u5b50\u5b9a\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u65ad\u8a00 x=2 \u662f\u591a\u9879\u5f0f P(x) \u7684\u6839\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Factorizacion-de-polinomios-utilizando-el-teorema-del-factor\"><\/span>\u4f7f\u7528\u56e0\u5b50\u5b9a\u7406\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u56e0\u5b50\u5b9a\u7406\u7684\u53e6\u4e00\u4e2a\u5e94\u7528\u662f<strong>\u591a\u9879\u5f0f\u7684\u56e0\u5b50\u5206\u89e3<\/strong>\u3002\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u5b83\u662f\u4ec0\u4e48\uff0c\u56e0\u5f0f\u5206\u89e3\u591a\u9879\u5f0f\u610f\u5473\u7740\u5c06\u591a\u9879\u5f0f\u7684\u8868\u8fbe\u5f0f\u8f6c\u6362\u4e3a\u56e0\u5f0f\u4e58\u79ef\uff0c\u5373\u56e0\u5f0f\u5206\u89e3\u591a\u9879\u5f0f\u7b80\u5316\u4e86\u5176\u4ee3\u6570\u8868\u8fbe\u5f0f\u3002<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u56e0\u6b64\uff0c\u9636\u4e58\u5b9a\u7406\u8868\u660e\uff0c\u5982\u679c\u591a\u9879\u5f0f P(x) \u5bf9\u4e8e\u7ed9\u5b9a\u503c a \u6ee1\u8db3 P(a)=0\uff0c\u5219\u6240\u8ff0\u591a\u9879\u5f0f\u7684\u8868\u8fbe\u5f0f\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e58\u79ef P(x)=(xa)\u00b7 Q( x)\uff0c\u5176\u4e2d Q(x) \u662f\u591a\u9879\u5f0f P(x) \u9664\u4ee5 (xa) \u6240\u5f97\u7684\u591a\u9879\u5f0f\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/facteur-theoreme-preuve.jpg\" alt=\"\u56e0\u5b50\u5b9a\u7406\u7684\u8bc1\u660e\" class=\"wp-image-2199\" width=\"470\" height=\"157\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u9636\u4e58\u5b9a\u7406\u5bf9\u4ee5\u4e0b\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e7291b669031afd3421168b7662c71c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3+2x^2+4x+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ece\u524d\u9762\u7684\u591a\u9879\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053 x=-2 \u662f\u5b83\u7684\u6839\u4e4b\u4e00\uff0c\u56e0\u4e3a x=-2 \u7684\u591a\u9879\u5f0f\u7684\u6570\u503c\u7b49\u4e8e 0\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d94a4657a385e672badeabd7458b376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-2) &amp; =(-2)^3+2\\cdot (-2)^2+4\\cdot (-2)+8 \\\\[2ex] &amp; =-8+2\\cdot 4+4\\cdot (-2)+8 \\\\[2ex] &amp; = -8+8-8+8 \\\\[2ex] &amp; = 0 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u7528\u9c81\u83f2\u5c3c\u6cd5\u5219\u5c06\u591a\u9879\u5f0f P(x) \u9664\u4ee5 x \u5f62\u6210\u7684\u4e8c\u9879\u5f0f\u548c\u8be5\u6839\u6539\u53d8\u7b26\u53f7\u4e4b\u95f4\u7684\u503c\uff0c\u5373\u56e0\u5b50 (x+2)\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/theoreme-du-facteur-zero.jpg\" alt=\"\u96f6\u56e0\u5b50\u5b9a\u7406\u6307\u51fa\" class=\"wp-image-2201\" width=\"205\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6240\u4ee5\u591a\u9879\u5f0f\u9664\u6cd5\u7684\u5546\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8787f77c00f3813ff7e93f147ae7a8d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{P(x)}{x+2} =x^2+4\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"113\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6839\u636e\u56e0\u5b50\u5b9a\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u591a\u9879\u5f0f P(x) \u8868\u793a\u4e3a\u56e0\u5b50 (x+2) \u4e58\u4ee5\u4e4b\u524d\u9664\u6cd5\u5f97\u5230\u7684\u5546\u7684\u5f62\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a63580effbfd7304133453960e84843_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = (x+2) \\cdot (x^2+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"190\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5bf9\u591a\u9879\u5f0f P(x) \u8fdb\u884c\u4e86\u56e0\u5f0f\u5206\u89e3\uff0c\u4f46\u53ea\u662f\u90e8\u5206\u5206\u89e3\u3002\u4e3a\u4e86\u5b8c\u5168\u5206\u89e3\u591a\u9879\u5f0f\uff0c\u5fc5\u987b\u5e94\u7528\u66f4\u957f\u7684\u8fc7\u7a0b\u3002\u6211\u4eec\u5236\u4f5c\u4e86\u4e00\u4efd\u6307\u5357\uff0c\u9010\u6b65\u6559\u6388<a href=\"https:\/\/mathority.org\/cn\"><strong><span style=\"text-decoration: underline;\">\u5982\u4f55\u56e0\u5f0f\u5206\u89e3\u9c81\u83f2\u5c3c\u591a\u9879\u5f0f<\/span><\/strong><\/a>\uff0c\u6b64\u5916\uff0c\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4e86\u6240\u6709\u7c7b\u578b\u7684\u56e0\u5f0f\u5206\u89e3\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u56e0\u6b64\uff0c\u8bf7\u5355\u51fb\u94fe\u63a5\u4ee5\u4e86\u89e3\u5982\u4f55\u4ece\u96c6\u5408\u4e2d\u5206\u89e3\u591a\u9879\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-teorema-del-factor\"><\/span>\u5df2\u89e3\u51b3\u7684\u56e0\u5b50\u5b9a\u7406\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7136\u540e\uff0c\u6211\u4eec\u51c6\u5907\u4e86\u51e0\u4e2a\u5173\u4e8e\u56e0\u6570\u5b9a\u7406\u4e00\u6b65\u4e00\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u9898\uff0c\u4f9b\u5927\u5bb6\u7ec3\u4e60\uff0c\u4ece\u800c\u68c0\u9a8c\u81ea\u5df1\u662f\u5426\u7406\u89e3\u4e86\u8fd9\u4e2a\u5b9a\u7406\u3002\u6211\u4eec\u5efa\u8bae\u60a8\u5c1d\u8bd5\u81ea\u5df1\u505a\u4e00\u4e0b\uff0c\u7136\u540e\u770b\u770b\u60a8\u662f\u5426\u6b63\u786e\u7406\u89e3\u4e86\u89e3\u51b3\u65b9\u6848\u3002\u53e6\u5916\u4e0d\u8981\u5fd8\u8bb0\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u7684\u8bc4\u8bba\u4e2d\u5411\u6211\u4eec\u7559\u4e0b\u60a8\u7684\u95ee\u9898\uff01 \u2753\u2753\ud83d\udcac\ud83d\udcac<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u4f7f\u7528\u9636\u4e58\u5b9a\u7406\u6765\u67e5\u627e\u591a\u9879\u5f0f P(x) \u662f\u5426\u53ef\u4ee5\u88ab\u4e8c\u9879\u5f0f Q(x) \u6574\u9664\uff0c\u5982\u679c\u53ef\u4ee5\uff0c\u5219\u627e\u5230\u591a\u9879\u5f0f\u7684\u6839\u5e76\u5bf9\u5176\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d91041d9502129f8feb71f75ec493bab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=2x^3-4x^2+x-7 \\qquad \\qquad Q(x)=x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"372\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u591a\u9879\u5f0f\u9664\u6570Q(x)\u662f\u4ec5\u7531x\u548c\u72ec\u7acb\u9879\u7ec4\u6210\u7684\u4e8c\u9879\u5f0f\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u8bc1\u660e\u591a\u9879\u5f0f P(x) \u53ef\u4ee5\u901a\u8fc7\u9636\u4e58\u5b9a\u7406\u9664\u4ee5\u53e6\u4e00\u4e2a\u591a\u9879\u5f0f Q(x)\uff0c\u6211\u4eec\u5fc5\u987b\u5728\u9664\u6570\u591a\u9879\u5f0f\u6539\u53d8\u7b26\u53f7\u7684\u72ec\u7acb\u9879\u4e2d\u8bc4\u4f30\u591a\u9879\u5f0f P(x) \u7684\u6570\u503c\uff0c\u4e5f\u5c31\u662f\u8bf4\u5728 x=3 \u65f6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e8ac752f8e16fae1d66386e9d2a02a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(3) &amp; =2\\cdot 3^3-4\\cdot 3^2+3-7\\\\[2ex] &amp; = 2\\cdot 27-4\\cdot 9+3-7 \\\\[2ex] &amp; = 54-36+3-7\\\\[2ex] &amp; = 14 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"219\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> x=3\u5904\u7684\u591a\u9879\u5f0fP(x)\u7684\u6570\u503c\u76f8\u5f53\u4e8e14\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u4e0d\u540c\u4e8e\u96f6\u3002\u56e0\u6b64\uff0c\u6839\u636e\u56e0\u5b50\u5b9a\u7406\uff0cP(x) \u4e0d\u80fd\u88ab Q(x) \u6574\u9664\uff0c\u56e0\u4e3a\u9664\u6cd5\u7684\u4f59\u6570\u4e0d\u4e3a\u96f6\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u901a\u8fc7\u9636\u4e58\u5b9a\u7406\u627e\u51fa\u591a\u9879\u5f0f P(x) \u662f\u5426\u80fd\u88ab\u4e8c\u9879\u5f0f Q(x) \u6574\u9664\uff0c\u5982\u679c\u662f\uff0c\u5219\u627e\u5230\u591a\u9879\u5f0f P(x) \u7684\u6839\u5e76\u5bf9\u5176\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c66c882f468d9bf67c8ae19b9629a24c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3+5x^2+3x-1 \\qquad \\qquad Q(x)=x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"371\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u591a\u9879\u5f0f\u9664\u6570Q(x)\u662f\u4ec5\u7531x\u548c\u72ec\u7acb\u9879\u7ec4\u6210\u7684\u4e8c\u9879\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u9636\u4e58\u5b9a\u7406\u3002<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u68c0\u67e5\u591a\u9879\u5f0f P(x) \u662f\u5426\u53ef\u4ee5\u9664\u4ee5\u591a\u9879\u5f0f Q(x)\uff0c\u6211\u4eec\u5fc5\u987b\u627e\u5230\u591a\u9879\u5f0f Q(x) \u6539\u53d8\u7b26\u53f7\u7684\u72ec\u7acb\u9879\u7684\u591a\u9879\u5f0f P(x) \u7684\u6570\u503c\uff0c\u5373\u5373\uff0c\u5728 x=-1 \u5904\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34b63772a1b44bee2c746d94b6ca4785_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-1) &amp; =(-1)^3+5\\cdot (-1)^2+3\\cdot (-1)-1\\\\[2ex] &amp; = -1+5\\cdot 1+3\\cdot (-1)-1\\\\[2ex] &amp; = -1+5-3-1\\\\[2ex] &amp; = 0 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"315\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u6b64\u95ee\u9898\u4e2d\uff0cx=-1 \u5904\u591a\u9879\u5f0f\u7684\u6570\u503c\u4e3a\u96f6\uff0c\u56e0\u6b64 P(x) \u53ef\u88ab Q(x) \u6574\u9664\u3002<\/p>\n<p class=\"has-text-align-left\">\u90a3\u4e48\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9636\u4e58\u5b9a\u7406\u63a8\u5bfc\u51fax=-1\u662f\u591a\u9879\u5f0fP(x)\u7684\u6839\uff0c\u56e0\u4e3aP(x)\u5728x=-1\u5904\u7684\u6570\u503c\u6d88\u5931\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u7531\u4e8e x=-1 \u662f\u591a\u9879\u5f0f P(x) \u7684\u6839\uff0c\u56e0\u6b64\u8981\u5bf9\u5176\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u53ea\u9700\u5c06\u5176\u9664\u4ee5 x+1 \u5373\u53ef\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4f7f\u7528 Ruffini \u65b9\u6cd5\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/facteur-et-reste-theoreme-2.jpg\" alt=\"\u56e0\u6570\u4e0e\u4f59\u6570\u5b9a\u7406\" class=\"wp-image-2223\" width=\"212\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u8fd0\u884c\u7684\u7ed3\u679c\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7d359811cb1941ccb7181216d4eb2667_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+4x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u591a\u9879\u5f0f P(x) \u56e0\u5f0f\u5206\u89e3\u5982\u4e0b\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4793f7847d400b7df22361f6b856a0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = (x+1) \\cdot (x^2+4x-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"231\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4f7f\u7528\u9636\u4e58\u5b9a\u7406\u67e5\u627e\u591a\u9879\u5f0f P(x) \u662f\u5426\u53ef\u88ab\u4e8c\u9879\u5f0f Q(x) \u6574\u9664\uff0c\u5982\u679c\u662f\uff0c\u5219\u8fd8\u67e5\u627e\u591a\u9879\u5f0f P(x) \u7684\u6839\u5e76\u5bf9\u5176\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3aead584139f397504eb04454974899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3+5x^2+4x-6 \\qquad \\qquad Q(x)=x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"372\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9664Q(x)\u7684\u591a\u9879\u5f0f\u662f\u4ec5\u7531x\u548c\u72ec\u7acb\u9879\u6784\u6210\u7684\u4e8c\u9879\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u56e0\u5b50\u5b9a\u7406\u3002<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u68c0\u67e5\u591a\u9879\u5f0f P(x) \u662f\u5426\u53ef\u88ab\u591a\u9879\u5f0f Q(x) \u6574\u9664\uff0c\u6211\u4eec\u5fc5\u987b\u786e\u5b9a\u591a\u9879\u5f0f Q(x) \u6539\u53d8\u7b26\u53f7\u7684\u72ec\u7acb\u9879\u7684\u591a\u9879\u5f0f P(x) \u7684\u6570\u503c\uff0c\u5373 -\u5373 x =-3 \u65f6\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef8bb895fe041193d71351ffadb94f2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-3) &amp; =(-3)^3+5\\cdot (-3)^2+4\\cdot (-3)-6\\\\[2ex] &amp; = -27+5\\cdot 9+4\\cdot (-3)-6\\\\[2ex] &amp; = -27+45-12-6\\\\[2ex] &amp; = 0 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cx=-3 \u5904\u591a\u9879\u5f0f\u7684\u6570\u503c\u4e3a\u96f6\uff0c\u56e0\u6b64 P(x) \u5b9e\u9645\u4e0a\u53ef\u4ee5\u88ab Q(x) \u6574\u9664\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u4ece\u9636\u4e58\u5b9a\u7406\u63a8\u5bfc\u51fa x=-3 \u662f\u591a\u9879\u5f0f P(x) \u7684\u6839\uff0c\u56e0\u4e3a P(-3) \u7b49\u4e8e 0\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u7531\u4e8e x=-3 \u662f\u591a\u9879\u5f0f P(x) \u7684\u6839\uff0c\u56e0\u6b64\u8981\u56e0\u5f0f\u5206\u89e3\u5b83\uff0c\u6211\u4eec\u5fc5\u987b\u5c06\u5176\u9664\u4ee5 x+3\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u9c81\u83f2\u5c3c\u89c4\u5219\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/facteur-theoreme-factorisation-par-ruffini.jpg\" alt=\"\u56e0\u5f0f\u5b9a\u7406 \u56e0\u5f0f \u9c81\u83f2\u5c3c\" class=\"wp-image-2226\" width=\"216\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\">\u90a3\u4e48\u9664\u6cd5\u7684\u7ed3\u679c\u5c31\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-990e12f6ae2d0b9effdb52dfaea8edbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5bf9\u591a\u9879\u5f0f P(x) \u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4929cce053644c03cdafec2fbfd77008_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = (x+3) \\cdot (x^2+2x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"231\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p class=\"has-text-align-center\">\u60a8\u5982\u4f55\u770b\u5f85\u56e0\u5b50\u5b9a\u7406\uff1f\u4f60\u8ba4\u4e3a\u5b83\u5728\u4ee3\u6570\u4e2d\u6709\u7528\u5417\uff1f\u6211\u4eec\u5728\u8bc4\u8bba\u4e2d\u8bfb\u5230\u4e86\u4f60\uff01<br \/> \ud83d\udc40\u2b07\u2b07\u2b07\ud83d\udc40<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u56e0\u5b50\u5b9a\u7406\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c55\u793a\u4e86\u56e0\u5f0f\u5b9a\u7406\u7684\u7528\u9014\uff1a\u591a\u9879\u5f0f\u7684\u6574\u9664\u6027\u3001\u6c42\u6839\u3001\u56e0\u5f0f\u5206\u89e3\u591a\u9879\u5f0f\u7b49\u3002\u6700 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%9b%a0%e5%ad%90%e5%ae%9a%e7%90%86\/\"> <span class=\"screen-reader-text\">\u56e0\u5b50\u5b9a\u7406<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[16],"tags":[],"class_list":["post-314","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized 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