Answer
$f(x)=x^n+c^n$ 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 $f(-c)=(-c)^n+c^n=-c^n+c^n=0$ (when n is odd).
This implies that $f(x)=x^n+c^n$ has the factor of $x+c$ by the factor theorem.
