{"id":242521,"date":"2025-07-04T08:07:29","date_gmt":"2025-07-04T08:07:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242521"},"modified":"2025-07-04T08:07:31","modified_gmt":"2025-07-04T08:07:31","slug":"what-is-the-factored-form-of-the-polynomial-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/what-is-the-factored-form-of-the-polynomial-2\/","title":{"rendered":"What is the factored form of the polynomial"},"content":{"rendered":"\n<p>What is the factored form of the polynomial? x2 &#8211; 12x + 27? O (x + 4)(x + 3) (x &#8211; 4)(x + 3) O (X + 9)(x +ht (x &#8211; 9)(x-3) o<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To factor the quadratic polynomial x2\u221212x+27x^2 &#8211; 12x + 27&#215;2\u221212x+27, we need to express it as the product of two binomials of the form (x\u2212a)(x\u2212b)(x &#8211; a)(x &#8211; b)(x\u2212a)(x\u2212b). Here\u2019s how we can factor it step-by-step:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Look for two numbers that multiply to give the constant term (27) and add to give the coefficient of the middle term (-12).<\/h3>\n\n\n\n<p>The two numbers should satisfy the following conditions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Their product must be equal to the constant term, 27.<\/li>\n\n\n\n<li>Their sum must be equal to the middle term&#8217;s coefficient, -12.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find factor pairs of 27.<\/h3>\n\n\n\n<p>The factor pairs of 27 are:(1,27),(3,9),(\u22121,\u221227),(\u22123,\u22129)(1, 27), (3, 9), (-1, -27), (-3, -9)(1,27),(3,9),(\u22121,\u221227),(\u22123,\u22129)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Check which pair sums to -12.<\/h3>\n\n\n\n<p>From the factor pairs above, the pair that adds up to -12 is (\u22123)(-3)(\u22123) and (\u22129)(-9)(\u22129), since:\u22123+(\u22129)=\u221212-3 + (-9) = -12\u22123+(\u22129)=\u221212<\/p>\n\n\n\n<p>And also:\u22123\u00d7\u22129=27-3 \\times -9 = 27\u22123\u00d7\u22129=27<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Write the factored form.<\/h3>\n\n\n\n<p>Thus, the quadratic expression can be factored as:(x\u22123)(x\u22129)(x &#8211; 3)(x &#8211; 9)(x\u22123)(x\u22129)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The correct factorization of x2\u221212x+27x^2 &#8211; 12x + 27&#215;2\u221212x+27 is (x\u22123)(x\u22129)(x &#8211; 3)(x &#8211; 9)(x\u22123)(x\u22129).<\/p>\n\n\n\n<p><strong>Correct answer:<\/strong> (x\u22129)(x\u22123)(x &#8211; 9)(x &#8211; 3)(x\u22129)(x\u22123).<\/p>\n\n\n\n<p>This is the factored form, and the reasoning involves finding two numbers that multiply to 27 and add up to -12, allowing us to factor the quadratic expression effectively.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-249.jpeg\" alt=\"\" class=\"wp-image-242533\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is the factored form of the polynomial? x2 &#8211; 12x + 27? O (x + 4)(x + 3) (x &#8211; 4)(x + 3) O (X + 9)(x +ht (x &#8211; 9)(x-3) o The Correct Answer and Explanation is: To factor the quadratic polynomial x2\u221212x+27x^2 &#8211; 12x + 27&#215;2\u221212x+27, we need to express it as [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-242521","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242521","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=242521"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242521\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242521"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242521"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242521"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}