{"id":271987,"date":"2025-07-26T08:53:14","date_gmt":"2025-07-26T08:53:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271987"},"modified":"2025-07-26T08:53:16","modified_gmt":"2025-07-26T08:53:16","slug":"5x232x35","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/5x232x35\/","title":{"rendered":"5x^2+32x+35"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-768.png\" alt=\"\" class=\"wp-image-271988\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The image displays the mathematical expression:&nbsp;<strong>5x\u00b2 + 32x + 35<\/strong>.<\/p>\n\n\n\n<p>This expression is a quadratic trinomial. It is &#8220;quadratic&#8221; because the highest power of the variable x is 2 (the x\u00b2 term). It is a &#8220;trinomial&#8221; because it consists of three distinct terms: 5x\u00b2, 32x, and 35, all connected by addition. In the standard form of a quadratic, ax\u00b2 + bx + c, the coefficients for this specific expression are a = 5, b = 32, and c = 35.<\/p>\n\n\n\n<p>A common operation performed on such expressions is factoring, which involves rewriting it as a product of two or more simpler expressions, typically linear binomials. To factor 5x\u00b2 + 32x + 35, one can use the &#8220;ac method&#8221;. This involves finding two numbers that multiply to the product of a and c (5 \u00d7 35 = 175) and add up to b (32). The factors of 175 are pairs like (1, 175), (5, 35), and (7, 25). The pair (7, 25) is the correct choice because 7 + 25 = 32.<\/p>\n\n\n\n<p>Using this pair, we can rewrite the middle term, 32x, as 7x + 25x. The expression becomes 5x\u00b2 + 25x + 7x + 35. Now, we can factor by grouping. We group the first two terms and the last two terms: (5x\u00b2 + 25x) + (7x + 35). From the first group, we factor out the greatest common factor, 5x, to get 5x(x + 5). From the second group, we factor out 7 to get 7(x + 5). Since both parts share the common binomial factor (x + 5), we can complete the factoring process.<\/p>\n\n\n\n<p>The final factored form of the expression is (5x + 7)(x + 5). This factored form is equivalent to the original expression and is useful for solving quadratic equations or analyzing the graph of the corresponding function.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2115.jpeg\" alt=\"\" class=\"wp-image-271989\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The image displays the mathematical expression:&nbsp;5x\u00b2 + 32x + 35. This expression is a quadratic trinomial. It is &#8220;quadratic&#8221; because the highest power of the variable x is 2 (the x\u00b2 term). It is a &#8220;trinomial&#8221; because it consists of three distinct terms: 5x\u00b2, 32x, and 35, all connected [&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-271987","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271987","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=271987"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271987\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271987"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271987"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}