Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.2 Combining Functions - 3.2 Exercises: 23

Answer

$\text{Degree of Term 1: } 5 \\\text{Degree of Term 2: } 3 \\\text{Degree of Term 3: } 1 \\\text{Degree of the Polynomial: } 5$

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, $ 2a^2b^3+3ab^2-8b .$ $\bf{\text{Solution Details:}}$ The degree of a term is the sum of the exponents of the variables in a term. Hence, the degree of each term in the given polynomial expression above is \begin{array}{l}\require{cancel} \text{Term 1: } 2+3=5 \\\text{Term 2: } 1+2=3 \\\text{Term 3: } 1 .\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: } 5 \\\text{Degree of Term 2: } 3 \\\text{Degree of Term 3: } 1 \\\text{Degree of the Polynomial: } 5 .\end{array}
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