{"id":242536,"date":"2025-07-04T08:09:27","date_gmt":"2025-07-04T08:09:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242536"},"modified":"2025-07-04T08:09:29","modified_gmt":"2025-07-04T08:09:29","slug":"what-is-the-factored-form-of-the-polynomial-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/what-is-the-factored-form-of-the-polynomial-3\/","title":{"rendered":"What is the factored form of the polynomial"},"content":{"rendered":"\n

What is the factored form of the polynomial? x2 – 12x + 27<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The factored form of the quadratic polynomial x2\u221212x+27x^2 – 12x + 27×2\u221212x+27 is:(x\u22123)(x\u22129)(x – 3)(x – 9)(x\u22123)(x\u22129)<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To factor the quadratic expression x2\u221212x+27x^2 – 12x + 27×2\u221212x+27, we need to find two numbers that:<\/p>\n\n\n\n

    \n
  1. Multiply to give the constant term (27).<\/li>\n\n\n\n
  2. Add up to give the coefficient of the linear term (-12).<\/li>\n<\/ol>\n\n\n\n

    Let\u2019s break it down step by step:<\/p>\n\n\n\n

      \n
    1. Start with the general form of a quadratic equation:<\/strong> ax2+bx+cax^2 + bx + cax2+bx+c In our case, a=1a = 1a=1, b=\u221212b = -12b=\u221212, and c=27c = 27c=27.<\/li>\n\n\n\n
    2. Look for two numbers that multiply to ac=1\u00d727=27ac = 1 \\times 27 = 27ac=1\u00d727=27 and add up to b=\u221212b = -12b=\u221212.<\/strong> We need two numbers that multiply to 27 and add to -12. These numbers are -3 and -9 because: (\u22123)\u00d7(\u22129)=27(-3) \\times (-9) = 27(\u22123)\u00d7(\u22129)=27 (\u22123)+(\u22129)=\u221212(-3) + (-9) = -12(\u22123)+(\u22129)=\u221212<\/li>\n\n\n\n
    3. Rewrite the middle term using these two numbers:<\/strong>
      The middle term, \u221212x-12x\u221212x, can be rewritten as \u22123x\u22129x-3x – 9x\u22123x\u22129x. Now, we have: x2\u22123x\u22129x+27x^2 – 3x – 9x + 27×2\u22123x\u22129x+27<\/li>\n\n\n\n
    4. Factor by grouping:<\/strong>
      Group the terms in pairs: (x2\u22123x)\u2212(9x\u221227)(x^2 – 3x) – (9x – 27)(x2\u22123x)\u2212(9x\u221227) Factor out the greatest common factor (GCF) from each pair: x(x\u22123)\u22129(x\u22123)x(x – 3) – 9(x – 3)x(x\u22123)\u22129(x\u22123)<\/li>\n\n\n\n
    5. Factor out the common binomial:<\/strong>
      Now that both terms contain the factor (x\u22123)(x – 3)(x\u22123), factor it out: (x\u22123)(x\u22129)(x – 3)(x – 9)(x\u22123)(x\u22129)<\/li>\n<\/ol>\n\n\n\n

      Thus, the factored form of x2\u221212x+27x^2 – 12x + 27×2\u221212x+27 is (x\u22123)(x\u22129)(x – 3)(x – 9)(x\u22123)(x\u22129).<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      What is the factored form of the polynomial? x2 – 12x + 27 The Correct Answer and Explanation is: The factored form of the quadratic polynomial x2\u221212x+27x^2 – 12x + 27×2\u221212x+27 is:(x\u22123)(x\u22129)(x – 3)(x – 9)(x\u22123)(x\u22129) Explanation: To factor the quadratic expression x2\u221212x+27x^2 – 12x + 27×2\u221212x+27, we need to find two numbers that: Let\u2019s […]<\/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-242536","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242536","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=242536"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242536\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}