{"id":208187,"date":"2025-04-26T08:36:22","date_gmt":"2025-04-26T08:36:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=208187"},"modified":"2025-04-26T08:36:25","modified_gmt":"2025-04-26T08:36:25","slug":"what-is-true-about-the-sum-of-the-two-polynomials","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/26\/what-is-true-about-the-sum-of-the-two-polynomials\/","title":{"rendered":"What is true about the sum of the two polynomials"},"content":{"rendered":"\n<p> What is true about the sum of the two polynomials? 6s^(2)t-2st^(2) 4s^(2)t-3st^(2) The sum is a binomial with a degree of 2. The sum is a binomial with a degree of 3. The sum is a trinomial with a degree of 2. The sum is a trinomial with a degree of 3.<\/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>Let&#8217;s solve the problem carefully first:<\/p>\n\n\n\n<p>You are asked:<br><strong>What is true about the sum of these two polynomials?<\/strong><br>Given polynomials:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( 6s^2t &#8211; 2st^2 )<\/li>\n\n\n\n<li>( 4s^2t &#8211; 3st^2 )<\/li>\n<\/ol>\n\n\n\n<p>First, <strong>add the polynomials together<\/strong> by combining like terms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Combine ( 6s^2t ) and ( 4s^2t ):<br>[<br>6s^2t + 4s^2t = 10s^2t<br>]<\/li>\n\n\n\n<li>Combine ( -2st^2 ) and ( -3st^2 ):<br>[<br>-2st^2 + (-3st^2) = -5st^2<br>]<\/li>\n<\/ul>\n\n\n\n<p>Thus, the sum is:<br>[<br>10s^2t &#8211; 5st^2<br>]<\/p>\n\n\n\n<p>Now, let&#8217;s answer the multiple-choice question.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify if it&#8217;s a binomial or trinomial.<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Binomial<\/strong> means <strong>two terms<\/strong>.<\/li>\n\n\n\n<li><strong>Trinomial<\/strong> means <strong>three terms<\/strong>.<\/li>\n\n\n\n<li>In our sum, ( 10s^2t ) and ( -5st^2 ) are <strong>two terms<\/strong> \u2192 <strong>Binomial<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the degree.<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>degree of a term<\/strong> is the sum of the exponents of all variables in that term.<\/li>\n\n\n\n<li>For ( 10s^2t ), degree = ( 2 + 1 = 3 ).<\/li>\n\n\n\n<li>For ( -5st^2 ), degree = ( 1 + 2 = 3 ).<\/li>\n<\/ul>\n\n\n\n<p>The <strong>degree of a polynomial<\/strong> is the highest degree among its terms, so the degree is <strong>3<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>\u2705 <strong>The sum is a binomial with a degree of 3.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">300-Word Explanation:<\/h3>\n\n\n\n<p>When adding polynomials, you combine like terms\u2014terms that have exactly the same variables raised to the same powers. In this case, the polynomials are ( 6s^2t &#8211; 2st^2 ) and ( 4s^2t &#8211; 3st^2 ).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First, combine the terms with ( s^2t ): ( 6s^2t + 4s^2t = 10s^2t ).<\/li>\n\n\n\n<li>Next, combine the terms with ( st^2 ): ( -2st^2 + (-3st^2) = -5st^2 ).<\/li>\n<\/ul>\n\n\n\n<p>Adding the polynomials results in:<br>[<br>10s^2t &#8211; 5st^2<br>]<\/p>\n\n\n\n<p>This new expression has exactly two terms: ( 10s^2t ) and ( -5st^2 ), meaning it is a <strong>binomial<\/strong> (because &#8220;bi-&#8221; means two).<\/p>\n\n\n\n<p>Next, determine the degree. The degree of a polynomial is based on the term with the highest total degree. For each term:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( 10s^2t ) has ( s ) raised to 2 and ( t ) raised to 1. Adding the exponents: ( 2 + 1 = 3 ).<\/li>\n\n\n\n<li>( -5st^2 ) has ( s ) raised to 1 and ( t ) raised to 2. Adding the exponents: ( 1 + 2 = 3 ).<\/li>\n<\/ul>\n\n\n\n<p>Both terms have a degree of 3. Therefore, the degree of the entire binomial is <strong>3<\/strong>.<\/p>\n\n\n\n<p>In conclusion, the sum is not a trinomial (three terms) nor a binomial with degree 2. The correct description is: <strong>The sum is a binomial with a degree of 3<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>What is true about the sum of the two polynomials? 6s^(2)t-2st^(2) 4s^(2)t-3st^(2) The sum is a binomial with a degree of 2. The sum is a binomial with a degree of 3. The sum is a trinomial with a degree of 2. The sum is a trinomial with a degree of 3. The correct answer [&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-208187","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/208187","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=208187"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/208187\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=208187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=208187"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=208187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}