{"id":274806,"date":"2025-07-28T12:06:43","date_gmt":"2025-07-28T12:06:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=274806"},"modified":"2025-07-28T12:06:45","modified_gmt":"2025-07-28T12:06:45","slug":"factor-the-expression-completely-48x-42","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/28\/factor-the-expression-completely-48x-42\/","title":{"rendered":"Factor the expression completely. 48x-42"},"content":{"rendered":"\n<p>Factor the expression completely. 48x-42<\/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 factor the expression 48x\u22124248x &#8211; 42, the first step is to find the greatest common factor (GCF) of the two terms.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the GCF<\/h3>\n\n\n\n<p>The two terms in the expression are 48x48x and \u221242-42. To find the GCF, look at the coefficients of the terms (48 and 42) and the variable part of 48x48x.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factorization of 48 is 48=24\u00d7348 = 2^4 \\times 3.<\/li>\n\n\n\n<li>The prime factorization of 42 is 42=2\u00d73\u00d7742 = 2 \\times 3 \\times 7.<\/li>\n<\/ul>\n\n\n\n<p>The common factors between 48 and 42 are 2 and 3. So, the GCF of 48 and 42 is 2\u00d73=62 \\times 3 = 6.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Factor out the GCF<\/h3>\n\n\n\n<p>Now that we know the GCF is 6, factor 6 out of the expression: 48x\u221242=6(8x\u22127)48x &#8211; 42 = 6(8x &#8211; 7)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Check if further factoring is possible<\/h3>\n\n\n\n<p>Now, examine the factored expression 6(8x\u22127)6(8x &#8211; 7). The term 8x\u221278x &#8211; 7 is a binomial, and it cannot be factored further because it does not have any common factors or special factoring patterns.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Factored Form<\/h3>\n\n\n\n<p>Thus, the completely factored form of the expression is: 6(8x\u22127)6(8x &#8211; 7)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>By finding the greatest common factor of the two terms, which is 6, and factoring it out, the expression 48x\u22124248x &#8211; 42 becomes 6(8x\u22127)6(8x &#8211; 7). This is the simplest and fully factored form of the expression. Factoring is useful because it simplifies expressions and is often a key step in solving equations or simplifying algebraic problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Factor the expression completely. 48x-42 The correct answer and explanation is: To factor the expression 48x\u22124248x &#8211; 42, the first step is to find the greatest common factor (GCF) of the two terms. Step 1: Find the GCF The two terms in the expression are 48x48x and \u221242-42. To find the GCF, look at the [&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-274806","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274806","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=274806"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274806\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=274806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=274806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=274806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}