{"id":227661,"date":"2025-06-06T10:46:53","date_gmt":"2025-06-06T10:46:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227661"},"modified":"2025-06-06T10:46:55","modified_gmt":"2025-06-06T10:46:55","slug":"which-statement-about-6x2-7x-10-is-true","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/which-statement-about-6x2-7x-10-is-true\/","title":{"rendered":"Which statement about 6×2 + 7x \u2013 10 is true"},"content":{"rendered":"\n

Which statement about 6×2 + 7x \u2013 10 is true? One of the factors is (x + 2). One of the factors is (3x \u2013 2). One of the factors is (2x + 5). One of the factors is (x \u2013 5).<\/p>\n\n\n\n

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

We are asked to determine which one of the following statements is true<\/strong> regarding a factor of this expression:<\/p>\n\n\n\n

    \n
  1. One of the factors is (x+2)(x + 2)(x+2)<\/li>\n\n\n\n
  2. One of the factors is (3x\u22122)(3x – 2)(3x\u22122)<\/li>\n\n\n\n
  3. One of the factors is (2x+5)(2x + 5)(2x+5)<\/li>\n\n\n\n
  4. One of the factors is (x\u22125)(x – 5)(x\u22125)<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Correct Answer:<\/strong><\/h3>\n\n\n\n

    One of the factors is (3x \u2013 2).<\/strong><\/p>\n\n\n\n

    \n\n\n\n

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

    To verify which factor is correct, we factor the quadratic expression:6×2+7x\u2212106x^2 + 7x – 106×2+7x\u221210<\/p>\n\n\n\n

    We use factoring by grouping. First, we multiply the leading coefficient 666 and the constant \u221210-10\u221210:6\u00d7(\u221210)=\u2212606 \\times (-10) = -606\u00d7(\u221210)=\u221260<\/p>\n\n\n\n

    Now, we need to find two numbers that multiply to \u221260-60\u221260 and add to the middle term +7+7+7. These numbers are +12<\/strong> and -5<\/strong> because:12\u00d7(\u22125)=\u221260,12+(\u22125)=712 \\times (-5) = -60,\\quad 12 + (-5) = 712\u00d7(\u22125)=\u221260,12+(\u22125)=7<\/p>\n\n\n\n

    Now rewrite the middle term using these two numbers:6×2+12x\u22125x\u2212106x^2 + 12x – 5x – 106×2+12x\u22125x\u221210<\/p>\n\n\n\n

    Group the terms:(6×2+12x)\u2212(5x+10)(6x^2 + 12x) – (5x + 10)(6×2+12x)\u2212(5x+10)<\/p>\n\n\n\n

    Factor each group:6x(x+2)\u22125(x+2)6x(x + 2) – 5(x + 2)6x(x+2)\u22125(x+2)<\/p>\n\n\n\n

    Factor out the common binomial:(6x\u22125)(x+2)(6x – 5)(x + 2)(6x\u22125)(x+2)<\/p>\n\n\n\n

    So the factorized form of 6×2+7x\u2212106x^2 + 7x – 106×2+7x\u221210 is:(6x\u22125)(x+2)(6x – 5)(x + 2)(6x\u22125)(x+2)<\/p>\n\n\n\n

    Now check the choices. We are told that one of the factors is (3x \u2013 2)<\/strong>. Let\u2019s test if this matches any part of our factorization.<\/p>\n\n\n\n

    Note:6x\u22125\u22603x\u22122(not equal)6x – 5 \\neq 3x – 2 \\quad \\text{(not equal)} 6x\u22125\ue020=3x\u22122(not equal)<\/p>\n\n\n\n

    Let\u2019s test multiplying (3x\u22122)(2x+5)(3x – 2)(2x + 5)(3x\u22122)(2x+5):(3x\u22122)(2x+5)=6×2+15x\u22124x\u221210=6×2+11x\u221210(3x – 2)(2x + 5) = 6x^2 + 15x – 4x – 10 = 6x^2 + 11x – 10(3x\u22122)(2x+5)=6×2+15x\u22124x\u221210=6×2+11x\u221210<\/p>\n\n\n\n

    That\u2019s not equal<\/strong> to 6×2+7x\u2212106x^2 + 7x – 106×2+7x\u221210, so (3x \u2013 2)<\/strong> is not<\/strong> a factor.<\/p>\n\n\n\n

    Let\u2019s test (2x+5)(2x + 5)(2x+5):(2x+5)(3x\u22122)=6×2+15x\u22124x\u221210=6×2+11x\u221210(still wrong)(2x + 5)(3x – 2) = 6x^2 + 15x – 4x – 10 = 6x^2 + 11x – 10 \\quad (\\text{still wrong})(2x+5)(3x\u22122)=6×2+15x\u22124x\u221210=6×2+11x\u221210(still wrong)<\/p>\n\n\n\n

    But we found that (x + 2) is a factor<\/strong>, from:(6x\u22125)(x+2)(6x – 5)(x + 2)(6x\u22125)(x+2)<\/p>\n\n\n\n

    So the correct answer is:<\/p>\n\n\n\n

    \ud83d\udc49 One of the factors is (x + 2)<\/strong><\/p>\n\n\n\n

    This matches choice 1<\/strong>, not (3x – 2)<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    \u2705 Final Answer:<\/h3>\n\n\n\n

    One of the factors is (x + 2).<\/strong><\/p>\n\n\n\n

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

    Which statement about 6×2 + 7x \u2013 10 is true? One of the factors is (x + 2). One of the factors is (3x \u2013 2). One of the factors is (2x + 5). One of the factors is (x \u2013 5). The Correct Answer and Explanation is: We are asked to determine which one […]<\/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-227661","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227661","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=227661"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227661\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}