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 $f(c)=c^n-c^n=0$, thus $x-c$ is a factor.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.