{"id":158078,"date":"2024-10-24T09:44:36","date_gmt":"2024-10-24T09:44:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=158078"},"modified":"2024-10-24T09:44:39","modified_gmt":"2024-10-24T09:44:39","slug":"which-expression-is-a-factor-of-10x2-11x-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/24\/which-expression-is-a-factor-of-10x2-11x-3\/","title":{"rendered":"Which expression is a factor of 10&#215;2 + 11x + 3"},"content":{"rendered":"\n<p>Which expression is a factor of 10&#215;2 + 11x + 3?<br>A. x \u2212 3<br>B. 2x + 1<br>C. 5x \u2212 3<br>D. 10x + 3<\/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 determine which expression is a factor of the quadratic polynomial (10x^2 + 11x + 3), we can use the factorization method. The goal is to express the quadratic in the form of ((ax + b)(cx + d)), where (a), (b), (c), and (d) are constants.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the coefficients<\/h3>\n\n\n\n<p>The polynomial is in the standard form (ax^2 + bx + c):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a = 10)<\/li>\n\n\n\n<li>(b = 11)<\/li>\n\n\n\n<li>(c = 3)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the AC method<\/h3>\n\n\n\n<p>The AC method involves finding two numbers that multiply to (a \\cdot c) (the product of the coefficient of (x^2) and the constant term) and add up to (b) (the coefficient of (x)).<\/p>\n\n\n\n<p>Here, (a \\cdot c = 10 \\cdot 3 = 30) and (b = 11).<\/p>\n\n\n\n<p>We need to find two numbers that multiply to (30) and add to (11):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The pairs of factors of (30) are: (1 \\times 30), (2 \\times 15), (3 \\times 10), (5 \\times 6).<\/li>\n\n\n\n<li>The pair that adds to (11) is (1) and (10) (since (1 + 10 = 11)).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Rewrite the middle term<\/h3>\n\n\n\n<p>Using these factors, we rewrite the polynomial as:<br>[<br>10x^2 + 10x + x + 3<br>]<br>Now, we group the terms:<br>[<br>(10x^2 + 10x) + (x + 3)<br>]<br>Factoring each group, we get:<br>[<br>10x(x + 1) + 1(x + 3)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Factor by grouping<\/h3>\n\n\n\n<p>We can factor out the common binomial:<br>[<br>(10x + 1)(x + 3)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Check the options<\/h3>\n\n\n\n<p>Now, let&#8217;s check the answer choices:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. (x &#8211; 3)<\/strong>: Not a factor.<\/li>\n\n\n\n<li><strong>B. (2x + 1)<\/strong>: Not a factor.<\/li>\n\n\n\n<li><strong>C. (5x &#8211; 3)<\/strong>: Not a factor.<\/li>\n\n\n\n<li><strong>D. (10x + 3)<\/strong>: Part of the factorization, but it needs to be (10x + 1).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>None of the provided options are direct factors. However, we can see that the factorization leads us to identify factors of the original polynomial. The complete factorization shows that (10x + 1) and (x + 3) are the factors. To verify, we can also use synthetic division or the quadratic formula, confirming that the expression can be factored, and indeed we notice that (10x^2 + 11x + 3) has no direct matches in the options. Therefore, no answer choice from the given options is correct based on this factorization process.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is a factor of 10&#215;2 + 11x + 3?A. x \u2212 3B. 2x + 1C. 5x \u2212 3D. 10x + 3 The Correct Answer and Explanation is: To determine which expression is a factor of the quadratic polynomial (10x^2 + 11x + 3), we can use the factorization method. The goal is to [&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-158078","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/158078","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=158078"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/158078\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=158078"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=158078"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=158078"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}