Answer
See below.
Work Step by Step
The factor theorem says that if f(c)=0, then (x-c) is a factor of f(x) and if (x-c) is a factor of f(x), then f(c)=0.
Hence if $f(x)=x^n+c^n$, then $f(-c)=(-c)^n+c^n=0$ if $n$ is odd, thus $x-c$ is a factor.
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 389: 112
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