{"id":245917,"date":"2025-07-06T14:53:15","date_gmt":"2025-07-06T14:53:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245917"},"modified":"2025-07-06T14:53:17","modified_gmt":"2025-07-06T14:53:17","slug":"what-does-it-mean-to-factor-completely","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/what-does-it-mean-to-factor-completely\/","title":{"rendered":"What does it mean to factor completely"},"content":{"rendered":"\n

What does it mean to factor completely<\/p>\n\n\n\n

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

“Factoring completely” refers to the process of breaking down an expression (typically a polynomial) into a product of simpler factors, where the expression is expressed as a multiplication of irreducible factors. These irreducible factors cannot be factored any further. The goal is to reach the simplest form where no further factoring can be done.<\/p>\n\n\n\n

For example, consider the polynomial expression 6×2+11x\u2212356x^2 + 11x – 356×2+11x\u221235. To factor this completely, you follow these steps:<\/p>\n\n\n\n

    \n
  1. Find the GCF (Greatest Common Factor)<\/strong>: Look for the largest common factor of all terms. In this case, there is no common factor across all terms, so we proceed to the next step.<\/li>\n\n\n\n
  2. Factor using grouping<\/strong> (if applicable) or apply methods like trial and error or the AC method (splitting the middle term). For 6×2+11x\u2212356x^2 + 11x – 356×2+11x\u221235, the AC method works:\n
      \n
    • Multiply the coefficient of x2x^2×2 (6) by the constant term (-35), which gives -210.<\/li>\n\n\n\n
    • Find two numbers that multiply to -210 and add up to 11. These numbers are 21 and -10.<\/li>\n\n\n\n
    • Rewrite the middle term: 6×2+21x\u221210x\u2212356x^2 + 21x – 10x – 356×2+21x\u221210x\u221235.<\/li>\n\n\n\n
    • Group: (6×2+21x)\u2212(10x+35)(6x^2 + 21x) – (10x + 35)(6×2+21x)\u2212(10x+35).<\/li>\n\n\n\n
    • Factor each group: 3x(2x+7)\u22125(2x+7)3x(2x + 7) – 5(2x + 7)3x(2x+7)\u22125(2x+7).<\/li>\n\n\n\n
    • Factor out the common binomial factor: (3x\u22125)(2x+7)(3x – 5)(2x + 7)(3x\u22125)(2x+7).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Check for irreducibility<\/strong>: After factoring, ensure that neither 3x\u221253x – 53x\u22125 nor 2x+72x + 72x+7 can be factored further. Since they cannot, the factorization is complete.<\/li>\n<\/ol>\n\n\n\n

      Thus, factoring completely means fully simplifying the expression by finding all possible factors and leaving them in their simplest irreducible form.<\/p>\n\n\n\n

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

      What does it mean to factor completely The Correct Answer and Explanation is: “Factoring completely” refers to the process of breaking down an expression (typically a polynomial) into a product of simpler factors, where the expression is expressed as a multiplication of irreducible factors. These irreducible factors cannot be factored any further. The goal is […]<\/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-245917","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245917","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=245917"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245917\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}