{"id":38850,"date":"2025-06-26T13:40:18","date_gmt":"2025-06-26T13:40:18","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=38850"},"modified":"2025-06-26T13:40:19","modified_gmt":"2025-06-26T13:40:19","slug":"name-the-polynomial-4x5-6x2-3-fifth-degree-binomial-fifth-degree-monomial-fifth-degree-trinomial-not-a-polynomial","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/name-the-polynomial-4x5-6x2-3-fifth-degree-binomial-fifth-degree-monomial-fifth-degree-trinomial-not-a-polynomial\/","title":{"rendered":"Name the polynomial: 4x^5 + 6x^2 + 3 – Fifth-degree binomial – Fifth-degree monomial – Fifth-degree trinomial – Not a polynomial"},"content":{"rendered":"\n

Name the polynomial: 4x^5 + 6x^2 + 3 – Fifth-degree binomial – Fifth-degree monomial – Fifth-degree trinomial – Not a polynomial<\/p>\n\n\n\n

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

Correct Answer: Fifth-degree trinomial<\/strong><\/p>\n\n\n\n

\n\n\n\n

The expression given is:<\/p>\n\n\n\n

4x\u2075 + 6x\u00b2 + 3<\/strong><\/p>\n\n\n\n

To name a polynomial, we consider two things:<\/p>\n\n\n\n

    \n
  1. Degree of the polynomial<\/strong><\/li>\n\n\n\n
  2. Number of terms in the expression<\/strong><\/li>\n<\/ol>\n\n\n\n

    Step 1: Determine the Degree<\/h3>\n\n\n\n

    The degree<\/strong> of a polynomial is the highest power of the variable (in this case, x) in the expression. Let’s look at each term:<\/p>\n\n\n\n

      \n
    • 4x\u2075 has degree 5<\/li>\n\n\n\n
    • 6x\u00b2 has degree 2<\/li>\n\n\n\n
    • 3 is a constant, so its degree is 0<\/li>\n<\/ul>\n\n\n\n

      The highest exponent is 5<\/strong>, so this is a fifth-degree<\/strong> polynomial.<\/p>\n\n\n\n

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

      A term<\/strong> is a part of a polynomial separated by a plus or minus sign.<\/p>\n\n\n\n

      The expression has:<\/p>\n\n\n\n

        \n
      • First term: 4x\u2075<\/li>\n\n\n\n
      • Second term: 6x\u00b2<\/li>\n\n\n\n
      • Third term: 3<\/li>\n<\/ul>\n\n\n\n

        That makes three terms<\/strong>.<\/p>\n\n\n\n

        Step 3: Use the Correct Terminology<\/h3>\n\n\n\n
          \n
        • A polynomial with one term is a monomial<\/strong><\/li>\n\n\n\n
        • A polynomial with two terms is a binomial<\/strong><\/li>\n\n\n\n
        • A polynomial with three terms is a trinomial<\/strong><\/li>\n<\/ul>\n\n\n\n

          Since this expression has three terms<\/strong>, it is a trinomial<\/strong>.<\/p>\n\n\n\n

          Final Name<\/h3>\n\n\n\n

          Putting both parts together:<\/p>\n\n\n\n

            \n
          • It is fifth-degree<\/strong><\/li>\n\n\n\n
          • It is a trinomial<\/strong><\/li>\n<\/ul>\n\n\n\n

            So, the correct classification is:<\/p>\n\n\n\n

            Fifth-degree trinomial<\/strong><\/p>\n\n\n\n

            Why the Other Choices Are Incorrect<\/h3>\n\n\n\n
              \n
            • Fifth-degree binomial<\/strong>: Incorrect because there are three terms, not two<\/li>\n\n\n\n
            • Fifth-degree monomial<\/strong>: Incorrect because there are three terms, not one<\/li>\n\n\n\n
            • Not a polynomial<\/strong>: Incorrect because the expression only contains whole number exponents and valid terms, which means it is indeed a polynomial<\/li>\n<\/ul>\n\n\n\n

              Therefore, the correct and complete name is fifth-degree trinomial<\/strong>.<\/p>\n\n\n\n

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

              Name the polynomial: 4x^5 + 6x^2 + 3 – Fifth-degree binomial – Fifth-degree monomial – Fifth-degree trinomial – Not a polynomial The Correct Answer and Explanation is: Correct Answer: Fifth-degree trinomial The expression given is: 4x\u2075 + 6x\u00b2 + 3 To name a polynomial, we consider two things: Step 1: Determine the Degree The degree […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38850","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38850"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38850\/revisions"}],"predecessor-version":[{"id":38852,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38850\/revisions\/38852"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}