{"id":155151,"date":"2024-10-15T20:01:08","date_gmt":"2024-10-15T20:01:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=155151"},"modified":"2024-10-15T20:01:10","modified_gmt":"2024-10-15T20:01:10","slug":"what-is-the-factored-form-of-the-polynomial","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/15\/what-is-the-factored-form-of-the-polynomial\/","title":{"rendered":"What is the factored form of the polynomial"},"content":{"rendered":"\n<p>What is the factored form of the polynomial?<\/p>\n\n\n\n<p>x2 \u2212 12x + 27?<\/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>To factor the polynomial (x^2 &#8211; 12x + 27), we can use the method of finding two numbers that multiply to the constant term (27) and add up to the coefficient of the linear term (-12).<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the Terms<\/strong>: The polynomial is in the standard quadratic form (ax^2 + bx + c), where:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a = 1)<\/li>\n\n\n\n<li>(b = -12)<\/li>\n\n\n\n<li>(c = 27)<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Find the Product and Sum<\/strong>: We need to find two numbers that:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply to (c) (27)<\/li>\n\n\n\n<li>Add to (b) (-12)<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Listing Factor Pairs of 27<\/strong>: The factor pairs of 27 are:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1 \\times 27)<\/li>\n\n\n\n<li>(3 \\times 9)<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Evaluate Factor Pairs<\/strong>: Next, we check which pair adds up to -12:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1 + 27 = 28)<\/li>\n\n\n\n<li>(3 + 9 = 12) We notice that neither pair yields -12. However, since we need the factors to also be negative (as the linear term&#8217;s coefficient is negative), we can instead consider:<\/li>\n\n\n\n<li>(-3) and (-9)<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Confirm the Factors<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply: ((-3) \\times (-9) = 27)<\/li>\n\n\n\n<li>Add: ((-3) + (-9) = -12) These values meet both criteria.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Write the Factored Form<\/strong>: We can now express the polynomial in its factored form. The original polynomial (x^2 &#8211; 12x + 27) can be factored as:<br>[<br>(x &#8211; 3)(x &#8211; 9)<br>]<\/li>\n\n\n\n<li><strong>Verification<\/strong>: To ensure our factorization is correct, we can expand ( (x &#8211; 3)(x &#8211; 9) ):<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Using the distributive property:<br>[<br>(x &#8211; 3)(x &#8211; 9) = x^2 &#8211; 9x &#8211; 3x + 27 = x^2 &#8211; 12x + 27<br>]<br>This confirms our factored form is correct.<\/li>\n<\/ul>\n\n\n\n<p>In conclusion, the polynomial (x^2 &#8211; 12x + 27) can be factored into the form ((x &#8211; 3)(x &#8211; 9)). This process highlights the importance of finding appropriate factors that satisfy both multiplication and addition requirements, leading to an accurate and simplified expression.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the factored form of the polynomial? x2 \u2212 12x + 27? The Correct Answer and Explanation is : To factor the polynomial (x^2 &#8211; 12x + 27), we can use the method of finding two numbers that multiply to the constant term (27) and add up to the coefficient of the linear term [&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-155151","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155151","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=155151"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155151\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}