{"id":5248,"date":"2022-02-06T16:20:19","date_gmt":"2022-02-06T08:20:23","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/more_about_polynomials\/division_of_polynomials-2\/"},"modified":"2022-04-06T03:16:36","modified_gmt":"2022-04-05T19:16:36","slug":"remainder_theorem","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/more_about_polynomials\/remainder_theorem\/","title":{"rendered":"\u7406\u89e3\u9918\u5f0f\u5b9a\u7406"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"5248\" class=\"elementor elementor-5248\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6e6d9785 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6e6d9785\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-41dc1ba6\" data-id=\"41dc1ba6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f85ef80 elementor-widget elementor-widget-text-editor\" data-id=\"f85ef80\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>4.1 \u7406\u89e3 \u9918\u5f0f\u5b9a\u7406 (Understand the Remainder Theorem)<\/h2><p>\u9918\u5f0f\u5b9a\u7406 \u5605\u7528\u8655\u597d\u7c21\u55ae\uff1a<\/p><ul><li>\u5e6b\u6211\u54cb\u8a08\u7b97\u51fa\u201c\u7576\u4e00\u500b\u591a\u9805\u5f0f\u88ab (ax + b) \u9664\u5605\u6642\u5019\uff0c\u55f0\u9918\u6578\u4fc2\u5e7e\u591a\u201d<\/li><\/ul><p>\u5481\u5230\u5e95\u8981\u9ede\u8a08\u5462?\u00a0 \u6839\u64da\u9918\u5f0f\u5b9a\u7406\uff1a<\/p><ul><li><span style=\"color: #ff0000;\"><strong>\u7576\u4e00\u500b\u591a\u9805\u5f0f f(x) \u88ab (ax + b) \u9664\u5605\u6642\u5019\uff0c\u9918\u6578 \uff1d f(-b\/a)<\/strong><\/span><\/li><\/ul><p>\u7528\u8fd4\u524d\u97624.1\u5605\u4f8b\u5b50\u569f\u8b1b\u89e3\u3002\u7576\u201c4x<sup>3<\/sup> \u2013 2x<sup>2 <\/sup>+ 4x \u2013 6 \u00f7 (2x \u2013 3)\u201d\u5605\u6642\u5019\uff0c\u6211\u54cb\u53ef\u4ee5\u7747\u5230\uff1a<\/p><ul><li>f(x) = 4x<sup>3<\/sup> \u2013 2x<sup>2 <\/sup>+ 4x \u2013 6<\/li><li>ax + b = 2x \u2013 3<\/li><li>\u6240\u4ee5\uff0c\u9918\u6578 = f ( -(-3)\/2 ) = f (3\/2) = 4(3\/2)<sup>3<\/sup> \u2013 2(3\/2)<sup>2<\/sup> + 4(3\/2) \u2013 6 = 9\u3002<ul><li>\u7576\u7136\uff0c\u500b\u9918\u6578\u540c\u6211\u54cb\u7528\u9577\u9664\u6cd5\u8a08\u51fa\u569f\u5605\u4e00\u6a23\u3002<\/li><\/ul><\/li><\/ul><p>\u597d\u591a\u540c\u5b78\u90fd\u6703\u88ab\u9918\u5f0f\u5b9a\u7406\u500b\u5b9a\u7fa9\u5687\u89aa\u3002\u53eb\u4f62\u8a084x<sup>3<\/sup> \u2013 2x<sup>2 <\/sup>+ 4x \u2013 6 \u00f7 2x \u2013\u00a0 3\u5605\u9918\u6578\u90fd\u5514\u77e5\u9ede\u8a08\uff08\u56e0\u70ba\u5187\u8a71\u4f60\u77e5f(x)\u4fc2\u54a9\uff0c\u5c31\u7b97\u6709\u90fd\u5514\u8a18\u5f97\u8981\u4ee3\u54a9\u5165\u500bf(x)\u51fd\u6578\u5ea6\uff09\u3002<\/p><p>\u5176\u5be6\u5927\u5bb6\u53ef\u4ee5\u7528\u4ee5\u4e0b\u5605\u6b65\u9a5f\u53bb\u8a18 \u201c\u9ede\u8a08\u500b\u9918\u6578\u201d\uff1a<\/p><ol><li>\u5148\u55ba\u8349\u7a3f\u7d19\u4e0a\u5beb\u4f4e \u201c\u9664\u6578\u5f0f = 0\u201d \uff08\u55ba\u4f8b\u5b50\u5ea6\u5373\u4fc2 2x \u2013 3 = 0\uff09<\/li><li>\u7136\u5f8c\u89e3\u65b9\u7a0b\u3002<br \/>\u53ef\u6c42\u5f97\u00a0 x = 3\/2<\/li><li>\u4ee3\u201c\u65b9\u7a0b\u5605\u7b54\u6848\u201d\uff08\u5373x=3\/2\uff09 \u5165\u201c\u88ab\u9664\u6578\u201d\u5605\u591a\u9805\u5f0f\u5ea6\u3002<\/li><li>\u8a08\u5230\u5605\u6578\u503c\u5c31\u4fc2\u8981\u6c42\u5605\u9918\u6578<\/li><\/ol><p>\u4ee5\u4e0a\u5c31\u4fc2\u500b\u65b9\u6cd5\u3002\u660e\u767d\u5f8c\uff0c\u6211\u5730\u518d\u7747\u8fd4\u6210\u500b\u689d\u4f8b\u984c\u61c9\u9ede\u4f5c\u7b54\uff1a<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-97e05d0 elementor-widget elementor-widget-accordion\" data-id=\"97e05d0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1591\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1591\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">\\(\u6c42 4x^{3}-2x^{2}+4x-6 \u88ab 2x-3 \u9664\u6642\u7684\u9918\u6578\\)<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1591\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1591\"><p style=\"padding-left: 40px;\">\u6839\u64da\u9918\u5f0f\u5b9a\u7406\uff0c<br \/>\u9918\u6578 = 4(3\/2)<sup>3<\/sup> \u2013 2(3\/2)<sup>2\u00a0<\/sup>+ 4(3\/2) \u2013 6<br \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 9<\/p><p>\u7559\u610f\u6211\u54cb\u4fc2\u5514\u9808\u8981\u5beb\u4f4e\u55ba\u7b54\u984c\u7c3f\u5ea6\u6211\u54cb\u4fc2\u9ede\u8981\u77e5\u4ee3\u54a9\u6578\u5165\u500b\u88ab\u9664\u6578\u5ea6\u8a08\u9918\u6578\u5605\u3002<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-332e54b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"332e54b4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-181cbc7b\" data-id=\"181cbc7b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5673dee5 elementor-widget elementor-widget-text-editor\" data-id=\"5673dee5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i>\u00a0<a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/more_about_polynomials\/division_of_polynomials\/\">\u591a\u9805\u5f0f\u9664\u6cd5<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-3d104953\" data-id=\"3d104953\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7ccfedd6\" data-id=\"7ccfedd6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-514f5aac elementor-widget elementor-widget-text-editor\" data-id=\"514f5aac\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/more_about_polynomials\/factor_theorem\/\">\u56e0\u5f0f\u5b9a\u7406<\/a>\u00a0<i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4bfd21bc\" data-id=\"4bfd21bc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-20775dbc elementor-widget elementor-widget-sidebar\" data-id=\"20775dbc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-5 > ul > li > a, .custom-menu-widget .ocean_custom_menu-5 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-5.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">DSE\u6578\u5b78 &#8211; \u5fc5\u4fee\u90e8\u5206\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-5 left dropdown-hover\"><ul id=\"menu-dsemaths_core\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1744\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1744\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/course-analysis\/\" class=\"menu-link\">\u8ab2\u7a0b\u5206\u6790 (Core)<\/a><\/li>\n<li  id=\"menu-item-1745\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children dropdown menu-item-1745\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/\" class=\"menu-link\">\u5514\u597d\u4ee5\u70ba\u5514\u99db\u8003 &#8211; \u76ee\u9304 <span class=\"nav-arrow fa fa-angle-down\"><\/span><\/a>\n<ul class=\"sub-menu\">\n\t<li  id=\"menu-item-4067\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4067\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/solving-equation\/\" class=\"menu-link\">1. \u89e3\u65b9\u7a0b<\/a><\/li>\n\t<li  id=\"menu-item-4068\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4068\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/polynomials\/\" class=\"menu-link\">2. \u591a\u9805\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4069\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4069\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/laws-of-indices\/\" class=\"menu-link\">3. \u6307\u6578\u5b9a\u5f8b<\/a><\/li>\n\t<li  id=\"menu-item-4070\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4070\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/factorization\/\" class=\"menu-link\">4. \u56e0\u5f0f\u5206\u89e3<\/a><\/li>\n\t<li  id=\"menu-item-4071\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4071\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/formulae\/\" class=\"menu-link\">5. \u516c\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4072\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4072\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/percentage\/\" class=\"menu-link\">6. \u767e\u5206\u6cd5<\/a><\/li>\n\t<li  id=\"menu-item-4073\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4073\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/rate-and-ratio\/\" class=\"menu-link\">7. \u7387\u53ca\u6bd4<\/a><\/li>\n\t<li  id=\"menu-item-4074\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4074\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/functions\/\" class=\"menu-link\">8. \u51fd\u6578<\/a><\/li>\n\t<li  id=\"menu-item-4075\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4075\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/estimation\/\" class=\"menu-link\">9. \u4f30\u7b97<\/a><\/li>\n\t<li  id=\"menu-item-4076\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4076\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/inequalities\/\" class=\"menu-link\">10. \u4e0d\u7b49\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4077\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4077\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/coordinates\/\" class=\"menu-link\">11. \u5750\u6a19<\/a><\/li>\n\t<li  id=\"menu-item-4079\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4079\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/geometry\/\" class=\"menu-link\">12. \u6f14\u7e79\u63a8\u7406\u5e7e\u4f55<\/a><\/li>\n\t<li  id=\"menu-item-4080\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4080\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/trigonometry\/\" class=\"menu-link\">13. \u4e09\u89d2\u6bd4<\/a><\/li>\n\t<li  id=\"menu-item-4081\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4081\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/shapes\/\" class=\"menu-link\">14. \u5e73\u9762\u53ca\u7acb\u9ad4\u5716\u5f62<\/a><\/li>\n\t<li  id=\"menu-item-4082\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4082\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/15-probability\/\" class=\"menu-link\">15. \u6982\u7387<\/a><\/li>\n\t<li  id=\"menu-item-4083\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4083\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/16-statistics\/\" class=\"menu-link\">16. \u7d71\u8a08<\/a><\/li>\n<\/ul>\n<\/li>\n<li  id=\"menu-item-3231\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3231\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u6578\u8207\u4ee3\u6578<\/a><\/li>\n<li  id=\"menu-item-3241\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3241\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental-shape_n_space\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u5ea6\u91cf\u3001\u5716\u5f62\u8207\u7a7a\u9593<\/a><\/li>\n<li  id=\"menu-item-3246\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3246\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_data_handling\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u6578\u64da\u8655\u7406<\/a><\/li>\n<li  id=\"menu-item-3290\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3290\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental_algebra\/\" class=\"menu-link\">\u975e\u57fa\u790e &#8211; \u6578\u8207\u4ee3\u6578<\/a><\/li>\n<li  id=\"menu-item-3288\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3288\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental-shape_n_space\/\" class=\"menu-link\">\u975e\u57fa\u790e &#8211; \u5ea6\u91cf\u3001\u5716\u5f62\u8207\u7a7a\u9593<\/a><\/li>\n<li  id=\"menu-item-3289\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3289\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/non_fundamental_data_handling\/\" class=\"menu-link\">\u975e\u57fa\u790e &#8211; \u6578\u64da\u8655\u7406<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>4.1 \u7406\u89e3 \u9918\u5f0f\u5b9a\u7406 (Understand the Remainder Theorem) \u9918\u5f0f\u5b9a\u7406 \u5605\u7528\u8655 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