{"id":164910,"date":"2024-11-10T19:15:59","date_gmt":"2024-11-10T19:15:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=164910"},"modified":"2024-11-10T19:16:09","modified_gmt":"2024-11-10T19:16:09","slug":"fully-factorise-the-expression","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/10\/fully-factorise-the-expression\/","title":{"rendered":"Fully factorise the expression"},"content":{"rendered":"\n<p>Fully factorise the expression<br>2r\u00b2 +15r+7<\/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 fully factorise the quadratic expression ( 2r^2 + 15r + 7 ), we will follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the coefficients<\/h3>\n\n\n\n<p>The given quadratic expression is:<br>[<br>2r^2 + 15r + 7<br>]<br>This is in the form ( ax^2 + bx + c ), where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( a = 2 )<\/li>\n\n\n\n<li>( b = 15 )<\/li>\n\n\n\n<li>( c = 7 )<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Multiply ( a ) and ( c )<\/h3>\n\n\n\n<p>Next, we multiply the coefficient ( a ) by ( c ):<br>[<br>a \\times c = 2 \\times 7 = 14<br>]<br>We now need to find two numbers that multiply to give 14 (the product) and add up to give 15 (the middle term coefficient).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find factors of 14 that sum to 15<\/h3>\n\n\n\n<p>We need to find two numbers whose product is 14 and whose sum is 15. The factors of 14 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 and 14<\/li>\n\n\n\n<li>2 and 7<\/li>\n<\/ul>\n\n\n\n<p>The pair that adds up to 15 is ( 1 ) and ( 14 ), because:<br>[<br>1 + 14 = 15<br>]<br>and<br>[<br>1 \\times 14 = 14<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Split the middle term<\/h3>\n\n\n\n<p>We now rewrite the middle term ( 15r ) using the numbers 1 and 14:<br>[<br>2r^2 + 1r + 14r + 7<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Factor by grouping<\/h3>\n\n\n\n<p>Now, group the terms in pairs:<br>[<br>(2r^2 + 1r) + (14r + 7)<br>]<br>Factor out the common factors from each group:<br>[<br>r(2r + 1) + 7(2r + 1)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 6: Factor out the common binomial<\/h3>\n\n\n\n<p>Both groups contain the common binomial factor ( (2r + 1) ). Factor this out:<br>[<br>(2r + 1)(r + 7)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>Thus, the fully factorised form of ( 2r^2 + 15r + 7 ) is:<br>[<br>(2r + 1)(r + 7)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This factorisation process is based on the method of splitting the middle term. First, we multiply the first and last coefficients ( ( a \\times c ) ), which gives us a product. We then find two numbers that multiply to this product and add to the middle coefficient. This allows us to split the middle term into two parts, making the expression easier to factor by grouping. Factoring by grouping involves taking common factors out of the pairs of terms. Finally, we factor out the common binomial, arriving at the fully factorised form.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fully factorise the expression2r\u00b2 +15r+7 The Correct Answer and Explanation is : To fully factorise the quadratic expression ( 2r^2 + 15r + 7 ), we will follow these steps: Step 1: Identify the coefficients The given quadratic expression is:[2r^2 + 15r + 7]This is in the form ( ax^2 + bx + c ), [&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-164910","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164910","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=164910"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164910\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}