Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.5 The Real Zeros of a Polynomial Function - 4.5 Assess Your Understanding - Page 233: 17


It is not a factor of $f(x).$

Work Step by Step

The Remainder Theorem says that the remainder when a function $f(x)$ is divided by $(x-r)$ is $f(r)$. Hence $f(-4)=4^7-64\cdot4^4-4^2-15=1\ne0$, therefore $(x+4)$ is not a factor of $f(x)$ by the factor theorem. The factor theorem says that if $f(c)=0$, then $(x-c)$ is a factor of $f(x)$ and vice versa.
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