{"id":27141,"date":"2021-03-28T13:00:24","date_gmt":"2021-03-28T13:00:24","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27141"},"modified":"2024-06-15T08:51:19","modified_gmt":"2024-06-15T08:51:19","slug":"%e5%ae%9e%e6%95%b0%e7%9a%84%e5%a4%9a%e9%a1%b9%e5%bc%8f%e4%bb%a3%e6%95%b0","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%ae%9e%e6%95%b0%e7%9a%84%e5%a4%9a%e9%a1%b9%e5%bc%8f%e4%bb%a3%e6%95%b0\/","title":{"rendered":"\u5b9e\u6570\u7684\u591a\u9879\u5f0f\u4ee3\u6570"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px; text-align:center;\">\n<h1>\u5b9e\u6570\u7684\u591a\u9879\u5f0f\u4ee3\u6570<\/h1>\n<p><em><strong>\u6458\u8981:<\/strong><br \/>\n        \u5728\u672c\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u7d22\u591a\u9879\u5f0f\u4ee3\u6570\u7684\u5b9a\u4e49\u3001\u6027\u8d28\u548c\u5e94\u7528\u3002\u591a\u9879\u5f0f\u662f\u6570\u5b66\u7684\u91cd\u8981\u7ec4\u6210\u90e8\u5206\uff0c\u5728\u5404\u4e2a\u5b66\u79d1\u4e2d\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002<br \/>\n    <\/em><\/p>\n<p>    <strong>\u5b66\u4e60\u76ee\u6807<\/strong><\/p>\n<p>\u5728\u672c\u8bfe\u7a0b\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<p style=\"text-align:left;\">\n        1. \u5b9a\u4e49\u5e76\u7406\u89e3\u591a\u9879\u5f0f\u53ca\u5176\u6027\u8d28\u3002<br \/>\n        2. \u8bc6\u522b\u591a\u9879\u5f0f\u7684\u6b21\u6570\u548c\u7cfb\u6570\u3002<br \/>\n        3. \u8fdb\u884c\u591a\u9879\u5f0f\u7684\u4ee3\u6570\u8fd0\u7b97\uff0c\u5e76\u5728\u6570\u5b66\u80cc\u666f\u4e2d\u5e94\u7528\u5176\u6027\u8d28\u3002\n    <\/p>\n<p>    <strong>\u5185\u5bb9\u7d22\u5f15:<\/strong><\/p>\n<p>\n        <a href=\"#1\"><strong>1. \u591a\u9879\u5f0f\u4ee3\u6570: \u5b9a\u4e49<\/strong><\/a><br \/>\n        <a href=\"#2\"><strong>2. \u591a\u9879\u5f0f\u7684\u7c7b\u578b<\/strong><\/a><br \/>\n        <a href=\"#3\"><strong>3. \u591a\u9879\u5f0f\u4ee3\u6570: \u8fd0\u7b97<\/strong><\/a><br \/>\n        <a href=\"#4\"><strong>4. \u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u548c\u9664\u6cd5<\/strong><\/a>\n    <\/p>\n<p>    <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ry4sKaS3RMc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2><strong>1. \u591a\u9879\u5f0f\u4ee3\u6570: \u5b9a\u4e49<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=139s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u8981\u7406\u89e3\u591a\u9879\u5f0f\u4ee3\u6570\uff0c\u9996\u5148\u6211\u4eec\u9700\u8981\u77e5\u9053\u4ec0\u4e48\u662f\u591a\u9879\u5f0f\u3002<\/span><\/strong><\/a> \u591a\u9879\u5f0f\u662f\u4ee3\u6570\u51fd\u6570\u3002\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u662f\u4e00\u4e2a\u5b9e\u53d8\u91cf\uff0c\u90a3\u4e48\u51fd\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u662f\u4e00\u4e2a\u591a\u9879\u5f0f\uff0c\u5982\u679c\u5b83\u53ef\u4ee5\u5199\u6210\uff1a\n<\/p>\n<p style=\"text-align: center; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(x)= \\sum_{i=0}^n a_i x^i= a_0 + a_1x + a_2x^2 + a_3x^3 + \\cdots + a_nx^n,<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u662f\u4e00\u4e2a\u975e\u8d1f\u6574\u6570\uff0c\u5e76\u4e14\u6240\u6709\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">a_i<\/span>\uff0c <span class=\"katex-eq\" data-katex-display=\"false\">i\\in\\{1,2,3,\\cdots,n\\},<\/span> \u90fd\u662f\u5b9e\u6570\u7cfb\u6570\u3002\u5982\u679c\u5b58\u5728\u4e00\u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u4f7f\u5f97 <span class=\"katex-eq\" data-katex-display=\"false\">a_k\\neq 0<\/span> \u5e76\u4e14\u5f53 <span class=\"katex-eq\" data-katex-display=\"false\">k\\lt i<\/span> \u65f6\uff0c <span class=\"katex-eq\" data-katex-display=\"false\">a_i=0<\/span>\uff0c\u90a3\u4e48\u8fd9\u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u503c\u79f0\u4e3a\u591a\u9879\u5f0f\u7684 <strong>\u6b21\u6570<\/strong>\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u591a\u9879\u5f0f\u7684\u6b21\u6570\u662f\u4f34\u968f\u975e\u96f6\u7cfb\u6570\u7684\u6700\u5927\u5e42\u3002\n<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2><strong>2. \u591a\u9879\u5f0f\u7684\u7c7b\u578b<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=340s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u591a\u9879\u5f0f\u6309\u5176\u6b21\u6570\u5206\u7c7b\uff1b<\/span><\/strong><\/a> \u56e0\u6b64\uff0c\u5f53\u63d0\u5230\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\uff0c\u901a\u5e38\u4f1a\u8bf4\u5b83\u662f\u4e00\u4e2a\u6b21\u6570\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u7684\u591a\u9879\u5f0f\uff0c\u5373 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u662f\u4f34\u968f\u975e\u96f6\u7cfb\u6570\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u7684\u6700\u5927\u5e42\u3002\n<\/p>\n<h3>2.1. \u5e38\u6570\u591a\u9879\u5f0f<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u662f\u5305\u62ec\u6240\u6709\u96f6\u6b21\u6570\u591a\u9879\u5f0f\u548c\u96f6\u591a\u9879\u5f0f\u7684\u5bb6\u65cf\u3002\u6211\u4eec\u8bf4\u4e00\u4e2a\u591a\u9879\u5f0f\u662f\u96f6\u6b21\u6570\u7684\uff0c\u5982\u679c\u5b83\u53ef\u4ee5\u5199\u6210 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=c,<\/span> \u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">c\\neq 0.<\/span> \u53e6\u4e00\u65b9\u9762\uff0c\u96f6\u591a\u9879\u5f0f\u7684\u5f62\u5f0f\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 0<\/span>\uff0c\u5b83\u6ca1\u6709\u5b9a\u4e49\u6b21\u6570\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2><strong>3. \u591a\u9879\u5f0f\u4ee3\u6570: \u8fd0\u7b97<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=428s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u591a\u9879\u5f0f\u7ee7\u627f\u4e86\u5b9e\u6570\u4ee3\u6570\u7684\u6240\u6709\u6027\u8d28\u3002<\/span><\/strong><\/a> \u7279\u522b\u91cd\u8981\u7684\u662f\u5206\u914d\u6027\u8d28\u548c\u7ed3\u5408\u6027\u8d28\u3002\n<\/p>\n<h3>3.1. \u52a0\u6cd5\u548c\u51cf\u6cd5<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=470s\" target=\"_blank\" rel=\"noopener\"> <strong><span style=\"color: #ff0000;\">\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> \u662f\u4e24\u4e2a\u6b21\u6570\u5206\u522b\u4e3a<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u7684\u591a\u9879\u5f0f\uff0c\u5206\u522b\u4e3a<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">m=n+k<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">0\\leq k,<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u90a3\u4e48\u4f1a\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle P(x) \\pm Q(x) &amp;=\\displaystyle \\sum_{i=0}^n a_i x^i \\pm \\sum_{i=0}^m b_i x^i \\\\ \\\\\n\n &amp;\\displaystyle = \\sum_{i=0}^n a_i x^i \\pm \\left( \\sum_{i=0}^n b_i x^i + \\sum_{i=n+1}^{n+k} b_i x^i \\right) \\\\ \\\\\n\n&amp;\\displaystyle = \\sum_{i=0}^n (a_i \\pm b_i) x^i + \\sum_{i=n+1}^m b_i x^i\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f34\u968f\u76f8\u540c\u5e42\u6b21 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u7684\u7cfb\u6570\u76f8\u52a0\u6216\u76f8\u51cf\uff0c\u6839\u636e\u60c5\u51b5\u800c\u5b9a\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\">\u4f8b\u5b50\uff1a<\/span><br \/>\n\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3+5x+2x^2<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 6x-3x^2 +23x^5<\/span>\uff0c\u90a3\u4e48\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">P(x) + Q(x) = \\cdots \\\\ = (3+5x+2x^2) + (6x-3x^2 +23x^5) \\\\ = 3 + (5+6)x + (2-3)x^2 + 23x^5 \\\\ = 3 + 11x - x^2 + 23x^5 <\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">P(x) - Q(x) = \\cdots \\\\ = (3+5x+2x^2) - (6x-3x^2 +23x^5) \\\\ = 3 + (5-6)x + (2+3)x^2 - 23x^5 \\\\ = 3 - x + 5x^2 - 23x^5 <\/span>\n<\/p>\n<h3>3.2. \u4e58\u6cd5<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=894s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5728\u4e0e\u591a\u9879\u5f0f\u52a0\u51cf\u6cd5\u76f8\u540c\u7684\u80cc\u666f\u4e0b\uff0c<\/span><\/strong><\/a> \u591a\u9879\u5f0f\u7684\u4e58\u79ef\u5c06\u5982\u4e0b\u53d1\u5c55\uff1a\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u9996\u5148\u533a\u5206\u6807\u91cf\u4e58\u6cd5\u3002\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">c \\in \\mathbb{R},<\/span> \u90a3\u4e48\u6211\u4eec\u6709\uff1a\n<\/p>\n<p style=\"text-align: center; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle c P(x) = c \\sum_{i=0}^n a_i x^i =\\sum_{i=0}^n c a_i x^i <\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u7136\u540e\u6211\u4eec\u6709\u591a\u9879\u5f0f\u4e4b\u95f4\u7684\u4e58\u6cd5\uff1a\n<\/p>\n<p style=\"text-align: center; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\displaystyle P(x) Q(x) &amp;\\displaystyle = \\left( \\sum_{i=0}^n a_i x^i \\right) \\left(\\sum_{j=0}^m b_j x^j\\right) \\\\ \\\\\n\n&amp;=\\displaystyle \\left[\\sum_{j=0}^m \\left( \\sum_{i=0}^n a_i x^i \\right) b_j x^j\\right] \\\\ \\\\\n\n&amp;=\\displaystyle \\sum_{j=0}^m \\left( \\sum_{i=0}^n a_ib_j x^{i+j} \\right) \\\\ \\\\\n\n&amp;=\\displaystyle \\sum_{i,j=0}^{n,m} a_ib_j x^{i+j}\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\n    \u8fd9\u5c31\u662f\u6211\u4eec\u901a\u8fc7\u8868\u8fbe\u201c\u6240\u6709\u7684\u4e58\u79ef\u4e4b\u548c\u201d\u603b\u7ed3\u51fa\u6765\u7684\u5185\u5bb9\u3002\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span style=\"color: #000080;\">\u4f8b\u5b50\uff1a<\/span><br \/>\n    \u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 4x+ 2x^2-x^4<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 5 - x + x^2-7x^3,<\/span> \u90a3\u4e48\uff1a\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">P(x)Q(x) =\\cdots \\\\ {} \\\\= (4x+ 2x^2-x^4)(5 - x + x^2-7x^3) \\\\ {} \\\\ = 4x(5 - x + x^2-7x^3) \\\\ + 2x^2 (5 - x + x^2-7x^3) \\\\ - x^4 (5 - x + x^2-7x^3) \\\\ {} \\\\ = 20x - 4x^2 + 4x^3 - 28x^4 \\\\ + 10x^2 - 2x^3 + 2x^4 - 14x^5 \\\\ -5x^4 + x^5 - x^6 + 7x^7 \\\\ {} \\\\ = 20x + 6x^2 + 2x^3 - 31x^4 - 13x^5 - x^6 + 7x^7<\/span>\n<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2><strong>4. \u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u548c\u9664\u6cd5<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1375s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u5f53\u6211\u4eec\u5c06\u4e24\u4e2a\u591a\u9879\u5f0f\u76f8\u4e58\u65f6\uff0c\u6211\u4eec\u662f\u4ece\u4e24\u4e2a\u7b80\u5355\u7684\u591a\u9879\u5f0f\u53d8\u6210\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u591a\u9879\u5f0f\uff08\u6b21\u6570\u66f4\u9ad8\uff09\u3002<\/span><\/strong><\/a> \u5f53\u6211\u4eec\u56e0\u5f0f\u5206\u89e3\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\uff0c\u6211\u4eec\u8fdb\u884c\u76f8\u53cd\u7684\u8fc7\u7a0b\uff1a\u5c06\u4e00\u4e2a\u590d\u6742\u7684\u591a\u9879\u5f0f\u53d8\u6210\u4e24\u4e2a\u6216\u66f4\u591a\u4f4e\u6b21\u591a\u9879\u5f0f\u7684\u4e58\u79ef\u3002\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u8981\u56e0\u5f0f\u5206\u89e3\u4e00\u4e2a\u591a\u9879\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span> \u5fc5\u987b\u627e\u5230\u4f7f\u591a\u9879\u5f0f\u4e3a\u96f6\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u503c\uff1b\u5982\u679c\u8fd9\u4e9b\u503c\u5b58\u5728\uff0c\u90a3\u4e48\u591a\u9879\u5f0f\u662f\u53ef\u5206\u89e3\u7684\u3002\u8c08\u8bba\u5b58\u5728\u6027\u662f\u53ef\u4ee5\u63a5\u53d7\u7684\uff0c\u4f46\u627e\u5230\u5b83\u4eec\u662f\u53e6\u4e00\u56de\u4e8b\u3002\u5f53\u6211\u4eec\u7814\u7a76\u4e8c\u6b21\u591a\u9879\u5f0f\u548c\uff082n\uff09\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u65f6\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u5ba1\u67e5\u8fd9\u4e2a\u95ee\u9898\u3002\n<\/p>\n<h3>4.1. \u7279\u6b8a\u4e58\u79ef<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1654s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u7136\u800c\uff0c\u6709\u4e9b\u60c5\u51b5\u4e0b\u56e0\u5f0f\u5206\u89e3\u5f88\u7b80\u5355\uff0c<\/span><\/strong><br \/>\n    <\/a> \u5982\u7279\u6b8a\u4e58\u79ef\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u7ed3\u679c\uff1a\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">x^2 - y^2 = (x-y)(x+y)<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">(x\\pm y)^2 = x^2 \\pm 2xy + y^2<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">(x \\pm y)^3 = x^3 \\pm 3x^2y + 3xy^2 \\pm y^3<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">x^3-y^3=(x-y)(x^2+xy+y^2)<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">x^3+y^3=(x+y)(x^2-xy+y^2)<\/span>\n<\/p>\n<h3>4. \u9664\u6cd5\u7b97\u6cd5<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1854s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u5c31\u50cf\u901a\u8fc7\u6574\u6570\u76f8\u4e58\u5f97\u5230\u590d\u5408\u6570\uff0c\u4f7f\u7528\u9664\u6cd5\u7b97\u6cd5\u5f53\u4f59\u6570\u4e3a\u96f6\u65f6\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c<\/span><\/strong><\/a> \u7c7b\u4f3c\u7684\u60c5\u51b5\u4e5f\u53d1\u751f\u5728\u591a\u9879\u5f0f\u4e0a\u3002\u7528\u6587\u672c\u89e3\u91ca\u9664\u6cd5\u7b97\u6cd5\u53ef\u80fd\u6709\u70b9\u590d\u6742\uff0c\u76f4\u63a5\u67e5\u770b\u5176\u6267\u884c\u60c5\u51b5\u548c\u7b97\u6cd5\u5728\u4f55\u79cd\u60c5\u51b5\u4e0b\u5bfc\u81f4\u56e0\u5f0f\u5206\u89e3\u8981\u5bb9\u6613\u5f97\u591a\u3002\u4e3a\u4e86\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5c06\u5ba1\u67e5\u4e00\u4e9b\u4f8b\u5b50\u3002\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span style=\"color: #000080;\">\u4f8b\u5b50\uff1a<\/span> \u8ba1\u7b97 <span class=\"katex-eq\" data-katex-display=\"false\">P(x):Q(x)<\/span> \u5bf9\u4e8e\u4ee5\u4e0b\u60c5\u51b5\uff1a\n<\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=2 x^3 + x^2 - 2 x - 1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x-1<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1930s\" target=\"_blank\" rel=\"noopener\"> <strong><span style=\"color: #ff0000;\">[\u89e3\u51b3\u65b9\u6848]<\/span><\/strong> <\/a>\n    <\/li>\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=x^4+2x^3-x+1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x^2-4<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=2120s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span> <\/a>\n    <\/li>\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=3 x^4 - 2 x^3 - x^2 - 4 x + 1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x^2+x+1<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=2331s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span> <\/a>\n    <\/li>\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=x^7+5x^4+5x^2-3x+1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x^3-2x^2+1<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=2464s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u89e3\u51b3\u65b9\u6848]<\/strong><\/span> <\/a>\n    <\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9e\u6570\u7684\u591a\u9879\u5f0f\u4ee3\u6570 \u6458\u8981: \u5728\u672c\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u7d22\u591a\u9879\u5f0f\u4ee3\u6570\u7684\u5b9a\u4e49\u3001\u6027\u8d28\u548c\u5e94\u7528\u3002\u591a\u9879\u5f0f\u662f\u6570\u5b66\u7684\u91cd\u8981\u7ec4\u6210\u90e8\u5206\uff0c\u5728\u5404\u4e2a\u5b66\u79d1\u4e2d\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002 \u5b66\u4e60\u76ee\u6807 \u5728\u672c\u8bfe\u7a0b\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a 1. \u5b9a\u4e49\u5e76\u7406\u89e3\u591a\u9879\u5f0f\u53ca\u5176\u6027\u8d28\u3002 2. \u8bc6\u522b\u591a\u9879\u5f0f\u7684\u6b21\u6570\u548c\u7cfb\u6570\u3002 3. \u8fdb\u884c\u591a\u9879\u5f0f\u7684\u4ee3\u6570\u8fd0\u7b97\uff0c\u5e76\u5728\u6570\u5b66\u80cc\u666f\u4e2d\u5e94\u7528\u5176\u6027\u8d28\u3002 \u5185\u5bb9\u7d22\u5f15: 1. \u591a\u9879\u5f0f\u4ee3\u6570: \u5b9a\u4e49 2. \u591a\u9879\u5f0f\u7684\u7c7b\u578b 3. \u591a\u9879\u5f0f\u4ee3\u6570: \u8fd0\u7b97 4. \u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u548c\u9664\u6cd5 1. \u591a\u9879\u5f0f\u4ee3\u6570: \u5b9a\u4e49 \u8981\u7406\u89e3\u591a\u9879\u5f0f\u4ee3\u6570\uff0c\u9996\u5148\u6211\u4eec\u9700\u8981\u77e5\u9053\u4ec0\u4e48\u662f\u591a\u9879\u5f0f\u3002 \u591a\u9879\u5f0f\u662f\u4ee3\u6570\u51fd\u6570\u3002\u5982\u679c \u662f\u4e00\u4e2a\u5b9e\u53d8\u91cf\uff0c\u90a3\u4e48\u51fd\u6570 \u662f\u4e00\u4e2a\u591a\u9879\u5f0f\uff0c\u5982\u679c\u5b83\u53ef\u4ee5\u5199\u6210\uff1a \u5176\u4e2d \u662f\u4e00\u4e2a\u975e\u8d1f\u6574\u6570\uff0c\u5e76\u4e14\u6240\u6709\u7684 \uff0c \u90fd\u662f\u5b9e\u6570\u7cfb\u6570\u3002\u5982\u679c\u5b58\u5728\u4e00\u4e2a \u4f7f\u5f97 \u5e76\u4e14\u5f53 \u65f6\uff0c \uff0c\u90a3\u4e48\u8fd9\u4e2a \u503c\u79f0\u4e3a\u591a\u9879\u5f0f\u7684 \u6b21\u6570\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u591a\u9879\u5f0f\u7684\u6b21\u6570\u662f\u4f34\u968f\u975e\u96f6\u7cfb\u6570\u7684\u6700\u5927\u5e42\u3002 2. \u591a\u9879\u5f0f\u7684\u7c7b\u578b \u591a\u9879\u5f0f\u6309\u5176\u6b21\u6570\u5206\u7c7b\uff1b \u56e0\u6b64\uff0c\u5f53\u63d0\u5230\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\uff0c\u901a\u5e38\u4f1a\u8bf4\u5b83\u662f\u4e00\u4e2a\u6b21\u6570\u4e3a \u7684\u591a\u9879\u5f0f\uff0c\u5373 \u662f\u4f34\u968f\u975e\u96f6\u7cfb\u6570\u7684 \u7684\u6700\u5927\u5e42\u3002 2.1. \u5e38\u6570\u591a\u9879\u5f0f \u8fd9\u662f\u5305\u62ec\u6240\u6709\u96f6\u6b21\u6570\u591a\u9879\u5f0f\u548c\u96f6\u591a\u9879\u5f0f\u7684\u5bb6\u65cf\u3002\u6211\u4eec\u8bf4\u4e00\u4e2a\u591a\u9879\u5f0f\u662f\u96f6\u6b21\u6570\u7684\uff0c\u5982\u679c\u5b83\u53ef\u4ee5\u5199\u6210 \u5176\u4e2d \u53e6\u4e00\u65b9\u9762\uff0c\u96f6\u591a\u9879\u5f0f\u7684\u5f62\u5f0f\u4e3a \uff0c\u5b83\u6ca1\u6709\u5b9a\u4e49\u6b21\u6570\u3002 3. \u591a\u9879\u5f0f\u4ee3\u6570: \u8fd0\u7b97 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27134,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[591,575],"tags":[],"class_list":["post-27141","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-591","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u5b9e\u6570\u7684\u591a\u9879\u5f0f\u4ee3\u6570 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u5b66\u4e60\u591a\u9879\u5f0f\u4ee3\u6570\uff1a\u5b9a\u4e49\u3001\u7c7b\u578b\u3001\u8fd0\u7b97\u3001\u4e58\u79ef\u3001\u56e0\u5f0f\u5206\u89e3\u548c\u9664\u6cd5\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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