{"id":17800,"date":"2020-04-11T20:12:50","date_gmt":"2020-04-11T20:12:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/?post_type=chapter&p=17800"},"modified":"2020-10-22T09:27:59","modified_gmt":"2020-10-22T09:27:59","slug":"summary-single-variable-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/summary-single-variable-polynomials\/","title":{"raw":"12.1.c - Summary: Defining Polynomials","rendered":"12.1.c – Summary: Defining Polynomials"},"content":{"raw":"In this section, we have learned the definition of a polynomial, how to evaluate a polynomial, and how to classify a polynomial according to the number of its terms and the degree of its highest exponent.\r\n

How to identify the degree and leading coefficient\u00a0of a polynomial expression<\/h3>\r\n
    \r\n \t
  1. Find the highest power of the variable (usually x) to determine the degree.<\/li>\r\n \t
  2. Identify the term containing the highest power of the variable to find the leading term.<\/li>\r\n \t
  3. Identify the coefficient of the leading term.<\/li>\r\n<\/ol>\r\n

    Degree of a Polynomial<\/h3>\r\n
      \r\n \t
    • The degree of a term is the exponent of its variable.<\/li>\r\n \t
    • The degree of a constant is [latex]0[\/latex].<\/li>\r\n \t
    • The degree of a polynomial is the highest degree of all its terms.<\/li>\r\n<\/ul>\r\n

      Glossary:<\/h2>\r\n
        \r\n \t
      • Polynomial<\/strong>\u00a0Algebraic expression that is created by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation.<\/li>\r\n \t
      • Monomial<\/strong>\u00a0\u00a0The basic building block of a polynomial. [latex]a{x}^{m}[\/latex], where [latex]a[\/latex] is a constant and [latex]m[\/latex] is a whole number.\u00a0\u00a0A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent.<\/li>\r\n \t
      • Binomial<\/strong>\u00a0\u00a0A polynomial containing exactly two terms.<\/li>\r\n \t
      • Trinomial<\/strong>\u00a0 A polynomial containing exactly three terms.<\/li>\r\n \t
      • Coefficient<\/strong>\u00a0 The number part of a term.<\/li>\r\n \t
      • Leading term<\/strong>\u00a0 The term with the highest degree.<\/li>\r\n \t
      • Leading coefficient<\/strong>\u00a0 The coefficient of the term with the highest degree.<\/li>\r\n \t
      • Standard form\u00a0<\/strong> When the terms of the polynomial are\u00a0arranged from the highest degree to the lowest degree.<\/li>\r\n<\/ul>","rendered":"

        In this section, we have learned the definition of a polynomial, how to evaluate a polynomial, and how to classify a polynomial according to the number of its terms and the degree of its highest exponent.<\/p>\n

        How to identify the degree and leading coefficient\u00a0of a polynomial expression<\/h3>\n
          \n
        1. Find the highest power of the variable (usually x) to determine the degree.<\/li>\n
        2. Identify the term containing the highest power of the variable to find the leading term.<\/li>\n
        3. Identify the coefficient of the leading term.<\/li>\n<\/ol>\n

          Degree of a Polynomial<\/h3>\n
            \n
          • The degree of a term is the exponent of its variable.<\/li>\n
          • The degree of a constant is [latex]0[\/latex].<\/li>\n
          • The degree of a polynomial is the highest degree of all its terms.<\/li>\n<\/ul>\n

            Glossary:<\/h2>\n
              \n
            • Polynomial<\/strong>\u00a0Algebraic expression that is created by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation.<\/li>\n
            • Monomial<\/strong>\u00a0\u00a0The basic building block of a polynomial. [latex]a{x}^{m}[\/latex], where [latex]a[\/latex] is a constant and [latex]m[\/latex] is a whole number.\u00a0\u00a0A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent.<\/li>\n
            • Binomial<\/strong>\u00a0\u00a0A polynomial containing exactly two terms.<\/li>\n
            • Trinomial<\/strong>\u00a0 A polynomial containing exactly three terms.<\/li>\n
            • Coefficient<\/strong>\u00a0 The number part of a term.<\/li>\n
            • Leading term<\/strong>\u00a0 The term with the highest degree.<\/li>\n
            • Leading coefficient<\/strong>\u00a0 The coefficient of the term with the highest degree.<\/li>\n
            • Standard form\u00a0<\/strong> When the terms of the polynomial are\u00a0arranged from the highest degree to the lowest degree.<\/li>\n<\/ul>\n","protected":false},"author":253111,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"4f4d10a080b94c69bc274009a30cab84","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-17800","chapter","type-chapter","status-publish","hentry"],"part":8336,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17800","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/253111"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17800\/revisions"}],"predecessor-version":[{"id":20391,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17800\/revisions\/20391"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/8336"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17800\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=17800"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=17800"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=17800"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=17800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}