TITLE: Prove that $x-1$ divides $x^n-1$
QUESTION [8 upvotes]: In algebra & polynomials, how do we prove that
$$x-1 \mid x^n -1?$$

REPLY [2 votes]: By Remainder theorem $ f(x) = x^n -1 ,$  if $ f(1) = 0$, then $ (x-1)$ is a factor of $f(x) $ .