{"id":187497,"date":"2025-02-05T04:06:03","date_gmt":"2025-02-05T04:06:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187497"},"modified":"2025-02-05T04:06:05","modified_gmt":"2025-02-05T04:06:05","slug":"classify-the-polynomial-by-degree-and-by-number-of-terms","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/05\/classify-the-polynomial-by-degree-and-by-number-of-terms\/","title":{"rendered":"Classify the polynomial by degree and by number of terms"},"content":{"rendered":"\n

Classify the polynomial by degree and by number of terms. 3x\u00c2\u00b2 The polynomial is a quadratic trinomial. cubic constant quadratic linear<\/p>\n\n\n\n

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

The given polynomial is 3x\u00b2<\/strong>. Let’s classify it based on its degree<\/strong> and number of terms<\/strong>.<\/p>\n\n\n\n

Step 1: Classifying by Degree<\/strong><\/h3>\n\n\n\n

The degree of a polynomial is determined by the highest power of the variable (x<\/strong>) in the expression.<\/p>\n\n\n\n

    \n
  • In 3x\u00b2<\/strong>, the exponent of x<\/strong> is 2<\/strong>.<\/li>\n\n\n\n
  • A polynomial with a degree of 2<\/strong> is called a quadratic polynomial<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Thus, 3x\u00b2 is a quadratic polynomial<\/strong>.<\/p>\n\n\n\n

    Step 2: Classifying by Number of Terms<\/strong><\/h3>\n\n\n\n

    The number of terms in a polynomial is determined by counting the individual terms separated by addition or subtraction.<\/p>\n\n\n\n

      \n
    • 3x\u00b2<\/strong> consists of only one term<\/strong>.<\/li>\n\n\n\n
    • A polynomial with one term<\/strong> is called a monomial<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Thus, 3x\u00b2 is a quadratic monomial<\/strong>.<\/p>\n\n\n\n

      Step 3: Correcting the Misclassification<\/strong><\/h3>\n\n\n\n

      The original classification stated that 3x\u00b2 is a quadratic trinomial<\/strong>, which is incorrect<\/strong> because:<\/p>\n\n\n\n

        \n
      • A trinomial<\/strong> must have exactly three terms<\/strong>.<\/li>\n\n\n\n
      • 3x\u00b2<\/strong> only has one term<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        The correct classification of 3x\u00b2<\/strong> is:<\/p>\n\n\n\n

          \n
        • Degree:<\/strong> Quadratic (since the highest exponent is 2).<\/li>\n\n\n\n
        • Number of terms:<\/strong> Monomial (since there is only one term).<\/li>\n<\/ul>\n\n\n\n

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

          3x\u00b2 is a quadratic monomial.<\/strong><\/p>\n\n\n\n

          Additional Explanation:<\/strong><\/h3>\n\n\n\n

          Here are some other classifications for reference:<\/p>\n\n\n\n

            \n
          • Linear Polynomial:<\/strong> Highest exponent is 1<\/strong> (e.g., 2x + 5<\/strong>).<\/li>\n\n\n\n
          • Quadratic Polynomial:<\/strong> Highest exponent is 2<\/strong> (e.g., x\u00b2 – 4x + 3<\/strong>).<\/li>\n\n\n\n
          • Cubic Polynomial:<\/strong> Highest exponent is 3<\/strong> (e.g., x\u00b3 + 2x\u00b2 – x + 7<\/strong>).<\/li>\n\n\n\n
          • Monomial:<\/strong> One term (e.g., 5x\u00b2<\/strong>).<\/li>\n\n\n\n
          • Binomial:<\/strong> Two terms (e.g., x\u00b2 + 4x<\/strong>).<\/li>\n\n\n\n
          • Trinomial:<\/strong> Three terms (e.g., x\u00b2 – 3x + 2<\/strong>).<\/li>\n<\/ul>\n\n\n\n

            Hope this helps! \ud83d\ude80<\/p>\n","protected":false},"excerpt":{"rendered":"

            Classify the polynomial by degree and by number of terms. 3x\u00c2\u00b2 The polynomial is a quadratic trinomial. cubic constant quadratic linear The Correct Answer and Explanation is : The given polynomial is 3x\u00b2. Let’s classify it based on its degree and number of terms. Step 1: Classifying by Degree The degree of a polynomial is […]<\/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-187497","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187497","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=187497"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187497\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}