{"id":156565,"date":"2024-10-17T11:50:46","date_gmt":"2024-10-17T11:50:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156565"},"modified":"2024-10-17T11:50:57","modified_gmt":"2024-10-17T11:50:57","slug":"which-are-factors-of-x2-4x-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/which-are-factors-of-x2-4x-5\/","title":{"rendered":"Which are factors of x2 \u2013 4x \u2013 5"},"content":{"rendered":"\n<p>Which are factors of x2 \u2013 4x \u2013 5? Check all that apply.<br>1.) (x \u2013 5)<br>2.) (x \u2013 4)<br>3.) (x \u2013 2)<br>4.) (x + 1)<br>5.) (x + 5)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is: <strong>Correct factors of (x^2 &#8211; 4x &#8211; 5) are: (x &#8211; 5) and (x + 1)<\/strong><\/p>\n\n\n\n<p>To determine the factors of the quadratic expression (x^2 &#8211; 4x &#8211; 5), we can use the factoring method. The general form of a quadratic equation is given by (ax^2 + bx + c). In our case:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a = 1)<\/li>\n\n\n\n<li>(b = -4)<\/li>\n\n\n\n<li>(c = -5)<\/li>\n<\/ul>\n\n\n\n<p>We need to find two numbers that multiply to (ac = 1 \\times (-5) = -5) and add up to (b = -4). The numbers that satisfy these conditions are (-5) and (1) because:<\/p>\n\n\n\n<p>[<br>-5 \\times 1 = -5 \\quad (\\text{product})<br>]<br>[<br>-5 + 1 = -4 \\quad (\\text{sum})<br>]<\/p>\n\n\n\n<p>Using these numbers, we can factor the quadratic as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Rewrite the middle term ((-4x)) using the two numbers found:<br>[<br>x^2 &#8211; 5x + x &#8211; 5<br>]<\/li>\n\n\n\n<li>Group the terms:<br>[<br>(x^2 &#8211; 5x) + (x &#8211; 5)<br>]<\/li>\n\n\n\n<li>Factor out the common factors from each group:<br>[<br>x(x &#8211; 5) + 1(x &#8211; 5)<br>]<\/li>\n\n\n\n<li>Now, factor out ((x &#8211; 5)):<br>[<br>(x &#8211; 5)(x + 1)<br>]<\/li>\n<\/ol>\n\n\n\n<p>Thus, the expression (x^2 &#8211; 4x &#8211; 5) factors to ((x &#8211; 5)(x + 1)).<\/p>\n\n\n\n<p>Now, we can evaluate the given options to check which are factors:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>(x \u2013 5)<\/strong>: This is a factor, as we found it in our factorization.<\/li>\n\n\n\n<li><strong>(x \u2013 4)<\/strong>: This is not a factor, as it does not appear in the factorization.<\/li>\n\n\n\n<li><strong>(x \u2013 2)<\/strong>: This is also not a factor, as it does not appear in the factorization.<\/li>\n\n\n\n<li><strong>(x + 1)<\/strong>: This is a factor, as it is part of our factorization.<\/li>\n\n\n\n<li><strong>(x + 5)<\/strong>: This is not a factor, as it does not appear in the factorization.<\/li>\n<\/ol>\n\n\n\n<p><strong>Correct factors of (x^2 &#8211; 4x &#8211; 5) are: (x &#8211; 5) and (x + 1)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which are factors of x2 \u2013 4x \u2013 5? Check all that apply.1.) (x \u2013 5)2.) (x \u2013 4)3.) (x \u2013 2)4.) (x + 1)5.) (x + 5) The Correct Answer and Explanation is : The correct answer is: Correct factors of (x^2 &#8211; 4x &#8211; 5) are: (x &#8211; 5) and (x + 1) [&hellip;]<\/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-156565","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156565","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=156565"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156565\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}