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.

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.