{"id":167812,"date":"2024-11-16T07:54:06","date_gmt":"2024-11-16T07:54:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167812"},"modified":"2024-11-16T07:54:08","modified_gmt":"2024-11-16T07:54:08","slug":"what-is-the-factored-form-of-x2-%e2%88%92-4x-%e2%88%92-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/16\/what-is-the-factored-form-of-x2-%e2%88%92-4x-%e2%88%92-5\/","title":{"rendered":"What is the factored form of x2 \u2212 4x \u2212 5"},"content":{"rendered":"\n<p>What is the factored form of x2 \u2212 4x \u2212 5?<br>(x + 5)(x \u2212 1)<br>(x + 5)(x + 1)<br>(x \u2212 5)(x \u2212 1)<br>(x \u2212 5)(x + 1)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the factored form of the quadratic expression (x^2 &#8211; 4x &#8211; 5), we need to factor it into two binomials. The standard approach involves finding two numbers that multiply to give the constant term (-5) and add to give the coefficient of the linear term (-4).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the necessary factors<\/h3>\n\n\n\n<p>The quadratic expression is in the form:<br>[<br>x^2 + bx + c<br>]<br>where (b = -4) and (c = -5). To factor the expression, we need to find two numbers that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply to give (c = -5)<\/li>\n\n\n\n<li>Add to give (b = -4)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the pair of numbers<\/h3>\n\n\n\n<p>We need to identify two numbers whose product is (-5) and whose sum is (-4). The factor pairs of (-5) are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1 \\times (-5))<\/li>\n\n\n\n<li>(-1 \\times 5)<\/li>\n<\/ul>\n\n\n\n<p>We now check which of these pairs add up to (-4):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1 + (-5) = -4)<\/li>\n\n\n\n<li>(-1 + 5 = 4)<\/li>\n<\/ul>\n\n\n\n<p>The pair (1) and (-5) works because:<br>[<br>1 + (-5) = -4 \\quad \\text{and} \\quad 1 \\times (-5) = -5<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Write the factored form<\/h3>\n\n\n\n<p>Since (1) and (-5) are the numbers that satisfy both conditions, we can factor the quadratic as:<br>[<br>x^2 &#8211; 4x &#8211; 5 = (x + 1)(x &#8211; 5)<br>]<\/p>\n\n\n\n<p>Thus, the correct factored form is:<br>[<br>(x + 1)(x &#8211; 5)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The factored form of (x^2 &#8211; 4x &#8211; 5) is ((x + 1)(x &#8211; 5)), which corresponds to option <strong>(x \u2212 5)(x + 1)<\/strong>. Factoring quadratics involves finding two numbers that multiply to the constant term and add to the coefficient of the linear term.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the factored form of x2 \u2212 4x \u2212 5?(x + 5)(x \u2212 1)(x + 5)(x + 1)(x \u2212 5)(x \u2212 1)(x \u2212 5)(x + 1) The Correct Answer and Explanation is: To find the factored form of the quadratic expression (x^2 &#8211; 4x &#8211; 5), we need to factor it into two binomials. [&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-167812","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167812","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=167812"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167812\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}