Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole

Chapter 3 - Exponents, Polynomials and Functions - 3.2 Combining Functions - 3.2 Exercises - Page 244: 25

Answer

$\text{Degree of Term 1: } 2 \\\text{Degree of Term 2: } 8 \\\text{Degree of Term 3: } 1 \\\text{Degree of Term 4: } 0 \\\text{Degree of the Polynomial: } 8$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of the degree of a term and the definition of the degree of a polynomial for the given polynomial, $\dfrac{2}{3}gh+\dfrac{1}{4}g^3h^5-\dfrac{2}{9}g+7 .$ $\bf{\text{Solution Details:}}$ The degree of a term is the sum of the exponents of the variables in the term. Hence, the degree of each term in the given polynomial expression above is \begin{array}{l}\require{cancel} \text{Term 1: } 1+1=2 \\\text{Term 2: } 3+5=8 \\\text{Term 3: } 1 \\\text{Term 4: } 0 .\end{array} The degree of a polynomial is the highest degree among all the terms. Hence, the given polynomial has the following characteristics: \begin{array}{l}\require{cancel} \text{Degree of Term 1: } 2 \\\text{Degree of Term 2: } 8 \\\text{Degree of Term 3: } 1 \\\text{Degree of Term 4: } 0 \\\text{Degree of the Polynomial: } 8 .\end{array}

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