Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

Chapter R - Elementary Algebra Review - R.4 Polynomials - R.4 Exercise Set: 31

Answer

$\text{First Term Coefficient: } -1 \\\text{First Term Degree: } 2+1=3 \\\\\text{Second Term Coefficient: } 4 \\\text{Second Term Degree: } 3 \\\\\text{Third Term Coefficient: } -2 \\\text{Third Term Degree: } 1+1=2 \\\\\text{Degree of the Polynomial: } 3$

Work Step by Step

The coefficient of a term is the number before the variable/s. The degree of a term is the sum of the exponents of all variables in a term. The degree of a polynomial is the highest degree among all the terms of the expression. Hence, the given expression, $-x^2y+4y^3-2xy ,$ has the following characteristics: \begin{array}{l}\require{cancel} \text{First Term Coefficient: } -1 \\\text{First Term Degree: } 2+1=3 \\\\\text{Second Term Coefficient: } 4 \\\text{Second Term Degree: } 3 \\\\\text{Third Term Coefficient: } -2 \\\text{Third Term Degree: } 1+1=2 \\\\\text{Degree of the Polynomial: } 3 .\end{array}

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