polynomials - Using induction for $x^n - 1$ is divisible by $x - 1$

Prove using induction that for all non-negative integers n and for all integers $ x > 1 $, $ x^n - 1 $ is divisible by $ x - 1 $.

Step 1: We will prove this using induction on n.
Step 2: Assume the claim is true when $ n = 1 $.
$$ x^{n+1} - 1 = x(x^n - 1) + (x - 1) $$

Can someone help me with this further?