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?