{"id":160894,"date":"2024-11-03T14:04:50","date_gmt":"2024-11-03T14:04:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=160894"},"modified":"2024-11-03T14:04:54","modified_gmt":"2024-11-03T14:04:54","slug":"factor-the-expression-using-the-gcf-15x-25","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/03\/factor-the-expression-using-the-gcf-15x-25\/","title":{"rendered":"Factor the expression using the GCF: 15x – 25"},"content":{"rendered":"\n

Factor the expression using the GCF: 15x – 25<\/p>\n\n\n\n

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

To factor the expression ( 15x – 25 ) using the Greatest Common Factor (GCF), we first need to identify the GCF of the coefficients and the variables present in the terms.<\/p>\n\n\n\n

    \n
  1. Identify the coefficients and terms:<\/strong>
    The expression ( 15x – 25 ) consists of two terms:<\/li>\n<\/ol>\n\n\n\n
      \n
    • The first term is ( 15x ).<\/li>\n\n\n\n
    • The second term is ( -25 ).<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Find the GCF of the coefficients:<\/strong><\/li>\n<\/ol>\n\n\n\n
          \n
        • The coefficient of the first term, ( 15 ), can be factored as ( 3 \\times 5 ).<\/li>\n\n\n\n
        • The coefficient of the second term, ( -25 ), can be factored as ( -1 \\times 5 \\times 5 ) or ( -1 \\times 5^2 ). Now, let’s find the GCF:<\/li>\n\n\n\n
        • The prime factors of ( 15 ) are ( 3 ) and ( 5 ).<\/li>\n\n\n\n
        • The prime factors of ( -25 ) are ( -1 ) and ( 5^2 ). The common factor between ( 15 ) and ( 25 ) is ( 5 ). Therefore, the GCF of the coefficients ( 15 ) and ( -25 ) is ( 5 ).<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Factor out the GCF:<\/strong>
            Next, we factor ( 5 ) out of each term in the expression:
            [
            15x – 25 = 5(3x) – 5(5) = 5(3x – 5)
            ]<\/li>\n\n\n\n
          2. Conclusion:<\/strong>
            The factored form of the expression ( 15x – 25 ) is ( 5(3x – 5) ).<\/li>\n<\/ol>\n\n\n\n

            Factoring out the GCF simplifies expressions and makes it easier to work with them in algebraic manipulations. In this case, the expression can be interpreted as the product of ( 5 ) and a binomial ( (3x – 5) ). This technique not only streamlines calculations but is also foundational in solving equations, graphing functions, and understanding polynomial behavior. Recognizing the GCF is a critical skill in algebra, helping to facilitate various operations such as solving equations and simplifying expressions.<\/p>\n","protected":false},"excerpt":{"rendered":"

            Factor the expression using the GCF: 15x – 25 The Correct Answer and Explanation is: To factor the expression ( 15x – 25 ) using the Greatest Common Factor (GCF), we first need to identify the GCF of the coefficients and the variables present in the terms. Factoring out the GCF simplifies expressions and makes […]<\/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-160894","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160894","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=160894"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160894\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}