Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 225: 111


$f(x)=x^n-c^n$ has the factor of $x-c$ by the factor theorem.

Work Step by Step

The factor theorem states that when $f(a)=0$, then we have $(x-a)$ as a factor of $f(x)$ and when $(x-a)$ is a factor of $f(x)$, then $f(a)=0$. Let us consider that $f(x)=x^n-c^n$ Then $f(c)=c^n-c^n=0$. This implies that $f(x)=x^n-c^n$ has the factor of $x-c$ by the factor theorem.
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