{"id":223960,"date":"2025-06-02T14:01:28","date_gmt":"2025-06-02T14:01:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223960"},"modified":"2025-06-02T14:01:30","modified_gmt":"2025-06-02T14:01:30","slug":"which-statement-is-true-about-the-polynomial-3x2y2-%e2%88%92-5xy2-%e2%88%92-3x2y2-2x2-after-it-has-been-fully-simplified-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/which-statement-is-true-about-the-polynomial-3x2y2-%e2%88%92-5xy2-%e2%88%92-3x2y2-2x2-after-it-has-been-fully-simplified-2\/","title":{"rendered":"Which statement is true about the polynomial 3x2y2 \u2212 5xy2 \u2212 3x2y2 + 2×2 after it has been fully simplified"},"content":{"rendered":"\n

Which statement is true about the polynomial 3x2y2 \u2212 5xy2 \u2212 3x2y2 + 2×2 after it has been fully simplified? It has 2 terms and a degree of 2. It has 2 terms and a degree of 3. It has 4 terms and a degree of 2. It has 4 terms and a degree of 4.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the correct answer, let’s simplify the polynomial<\/strong> first:<\/p>\n\n\n\n

Given:
3x\u00b2y\u00b2 \u2212 5xy\u00b2 \u2212 3x\u00b2y\u00b2 + 2x\u00b2<\/strong><\/p>\n\n\n\n

Step 1: Combine like terms<\/h3>\n\n\n\n

Look for like terms to simplify:<\/p>\n\n\n\n

    \n
  • 3x\u00b2y\u00b2<\/strong> and \u22123x\u00b2y\u00b2<\/strong> are like terms: 3x2y2\u22123x2y2=03x\u00b2y\u00b2 \u2212 3x\u00b2y\u00b2 = 0 So, these cancel out.<\/li>\n\n\n\n
  • Now we\u2019re left with: \u22125xy2+2×2\u22125xy\u00b2 + 2x\u00b2<\/li>\n<\/ul>\n\n\n\n

    This is the simplified form of the polynomial.<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Count the terms<\/h3>\n\n\n\n

    Each separate part (separated by ‘+’ or ‘\u2212’) is a term:<\/p>\n\n\n\n

      \n
    • \u22125xy\u00b2<\/strong> is one term.<\/li>\n\n\n\n
    • +2x\u00b2<\/strong> is another.<\/li>\n<\/ul>\n\n\n\n

      So, it has 2 terms<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Find the degree of the polynomial<\/h3>\n\n\n\n

      The degree of a polynomial<\/strong> is the highest sum of exponents of variables in any single term:<\/p>\n\n\n\n

        \n
      • \u22125xy\u00b2<\/strong> \u2192 x\u00b9y\u00b2 \u2192 degree = 1 + 2 = 3<\/strong><\/li>\n\n\n\n
      • 2x\u00b2<\/strong> \u2192 x\u00b2 \u2192 degree = 2<\/strong><\/li>\n<\/ul>\n\n\n\n

        So the highest degree is 3<\/strong>.<\/p>\n\n\n\n

        \n\n\n\n

        Final Answer:<\/h3>\n\n\n\n

        \u2705 It has 2 terms and a degree of 3.<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        Explanation <\/h3>\n\n\n\n

        A polynomial is an algebraic expression made up of terms connected by addition or subtraction, where each term is a product of a constant and variables raised to whole number powers. To analyze a polynomial, it is important to simplify it by combining like terms and then evaluate its structure.<\/p>\n\n\n\n

        The given polynomial is:
        3x\u00b2y\u00b2 \u2212 5xy\u00b2 \u2212 3x\u00b2y\u00b2 + 2x\u00b2<\/strong><\/p>\n\n\n\n

        We begin by combining like terms. The terms 3x\u00b2y\u00b2<\/strong> and \u22123x\u00b2y\u00b2<\/strong> are like terms because they have the same variables with the same exponents. These cancel each other out, resulting in 0. This simplifies the expression to:
        \u22125xy\u00b2 + 2x\u00b2<\/strong><\/p>\n\n\n\n

        Now we have two remaining terms. A term is any individual part of the expression, separated by plus or minus signs. Therefore, the polynomial has 2 terms<\/strong>.<\/p>\n\n\n\n

        Next, we determine the degree<\/strong> of the polynomial. The degree of each term is found by adding the exponents of all the variables in that term. For \u22125xy\u00b2<\/strong>, the exponents are 1 (on x) and 2 (on y), giving a total of 3. For 2x\u00b2<\/strong>, the exponent is 2. The degree of the entire polynomial is the highest degree among its terms, which is 3<\/strong>.<\/p>\n\n\n\n

        Thus, the fully simplified polynomial has 2 terms<\/strong> and a degree of 3<\/strong>.<\/p>\n\n\n\n

        \u2705 Correct answer: “It has 2 terms and a degree of 3.”<\/strong><\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Which statement is true about the polynomial 3x2y2 \u2212 5xy2 \u2212 3x2y2 + 2×2 after it has been fully simplified? It has 2 terms and a degree of 2. It has 2 terms and a degree of 3. It has 4 terms and a degree of 2. It has 4 terms and a degree of […]<\/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-223960","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223960","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=223960"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223960\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}