{"id":167905,"date":"2024-11-16T11:34:42","date_gmt":"2024-11-16T11:34:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167905"},"modified":"2024-11-16T11:34:44","modified_gmt":"2024-11-16T11:34:44","slug":"how-do-you-convert-a-quadratic-equation-from-standard-form-into-factored-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/16\/how-do-you-convert-a-quadratic-equation-from-standard-form-into-factored-form\/","title":{"rendered":"How do you convert a quadratic equation from standard form into factored form"},"content":{"rendered":"\n

How do you convert a quadratic equation from standard form into factored form?<\/p>\n\n\n\n

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

To convert a quadratic equation from standard form<\/strong> ( ax^2 + bx + c = 0 ) to factored form<\/strong> ( a(x – r_1)(x – r_2) = 0 ), follow these steps:<\/p>\n\n\n\n

Steps for Conversion:<\/h3>\n\n\n\n
    \n
  1. Factor out the greatest common factor (GCF)<\/strong> if possible.<\/li>\n\n\n\n
  2. Identify coefficients<\/strong>: ( a ), ( b ), and ( c ).<\/li>\n\n\n\n
  3. Find two numbers<\/strong> that multiply to ( a \\cdot c ) (the product of the leading coefficient and constant term) and add to ( b ) (the coefficient of ( x )).<\/li>\n\n\n\n
  4. Split the middle term<\/strong> using these two numbers to rewrite the quadratic as four terms.<\/li>\n\n\n\n
  5. Group terms in pairs<\/strong> and factor each pair.<\/li>\n\n\n\n
  6. Factor out the common binomial factor<\/strong> to get the factored form.<\/li>\n<\/ol>\n\n\n\n

    If the quadratic cannot be factored easily, use the quadratic formula<\/strong> to find the roots (( r_1 ) and ( r_2 )), and write the equation as ( a(x – r_1)(x – r_2) = 0 ).<\/p>\n\n\n\n

    \n\n\n\n

    Example:<\/h3>\n\n\n\n

    Convert ( 2x^2 + 5x + 3 = 0 ) to factored form.<\/p>\n\n\n\n

      \n
    1. Identify coefficients: ( a = 2 ), ( b = 5 ), ( c = 3 ).<\/li>\n\n\n\n
    2. Find two numbers that multiply to ( 2 \\cdot 3 = 6 ) and add to ( 5 ). These are ( 2 ) and ( 3 ).<\/li>\n\n\n\n
    3. Split the middle term: ( 2x^2 + 2x + 3x + 3 = 0 ).<\/li>\n\n\n\n
    4. Group terms: ( (2x^2 + 2x) + (3x + 3) = 0 ).<\/li>\n\n\n\n
    5. Factor each group: ( 2x(x + 1) + 3(x + 1) = 0 ).<\/li>\n\n\n\n
    6. Factor the common binomial: ( (2x + 3)(x + 1) = 0 ).<\/li>\n<\/ol>\n\n\n\n

      The factored form is ( (2x + 3)(x + 1) = 0 ).<\/p>\n\n\n\n

      \n\n\n\n

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

      Factoring simplifies quadratic equations to find their roots efficiently. The roots represent the values of ( x ) that make the equation zero, which are also the points where the graph intersects the ( x )-axis. This method is vital in algebra as it connects polynomial structure to its solutions and applications in real-world problems like projectile motion and optimization.<\/p>\n","protected":false},"excerpt":{"rendered":"

      How do you convert a quadratic equation from standard form into factored form? The Correct Answer and Explanation is: To convert a quadratic equation from standard form ( ax^2 + bx + c = 0 ) to factored form ( a(x – r_1)(x – r_2) = 0 ), follow these steps: Steps for Conversion: If […]<\/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-167905","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167905","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=167905"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167905\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167905"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167905"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}