{"id":234774,"date":"2025-06-14T12:53:21","date_gmt":"2025-06-14T12:53:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234774"},"modified":"2025-06-14T12:53:23","modified_gmt":"2025-06-14T12:53:23","slug":"solve-the-following-equation-by-factoring","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/solve-the-following-equation-by-factoring\/","title":{"rendered":"Solve the following equation by factoring."},"content":{"rendered":"\n

Solve the following equation by factoring.
Rewrite the equation in factored form.
(Type your answer in factored form.)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Answer:<\/strong>
(x+5)(x-8)<\/p>\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

To solve the quadratic equation x\u00b2 = 3x + 40 by factoring, the first step is to rearrange the equation into the standard quadratic form, which is ax\u00b2 + bx + c = 0. This is accomplished by moving all terms to one side of the equation, setting the expression equal to zero.<\/p>\n\n\n\n

Starting with the given equation:
x\u00b2 = 3x + 40<\/p>\n\n\n\n

Subtract 3x and 40 from both sides to bring all terms to the left side:
x\u00b2 – 3x – 40 = 0<\/p>\n\n\n\n

Now that the equation is in standard form, the next step is to factor the trinomial x\u00b2 – 3x – 40. The goal is to find two numbers that simultaneously satisfy two conditions:<\/p>\n\n\n\n

    \n
  1. They must multiply to the constant term, which is -40.<\/li>\n\n\n\n
  2. They must add up to the coefficient of the middle term (the x-term), which is -3.<\/li>\n<\/ol>\n\n\n\n

    Consider the pairs of integers that multiply to -40 and check their sum:<\/p>\n\n\n\n

      \n
    • 1 and -40 (Sum = -39)<\/li>\n\n\n\n
    • 2 and -20 (Sum = -18)<\/li>\n\n\n\n
    • 4 and -10 (Sum = -6)<\/li>\n\n\n\n
    • 5 and -8 (Sum = -3)<\/li>\n<\/ul>\n\n\n\n

      The pair 5 and -8 meets both requirements, as their product is -40 and their sum is -3. These two numbers are used to write the trinomial as a product of two binomials.<\/p>\n\n\n\n

      The factored form of the expression is (x + 5)(x – 8).<\/p>\n\n\n\n

      Therefore, the equation rewritten in factored form is:
      (x + 5)(x – 8) = 0<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      The expression (x + 5)(x – 8) is the correct answer for the box. The order of the factors can be reversed to (x – 8)(x + 5) and still be correct.<\/p>\n\n\n\n

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

      Solve the following equation by factoring.Rewrite the equation in factored form.(Type your answer in factored form.) The Correct Answer and Explanation is: Answer:(x+5)(x-8) Explanation: To solve the quadratic equation x\u00b2 = 3x + 40 by factoring, the first step is to rearrange the equation into the standard quadratic form, which is ax\u00b2 + bx + c = 0. […]<\/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-234774","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234774","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=234774"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234774\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234774"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234774"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}