Hi there,

I am trying to find the missing factor here:

$\displaystyle x^n - k^n = (x - k)(?)$

I have tried various things. First I tried to do it by construction, giving:

$\displaystyle x^n - k^n = (x - k)(x^{n-1} + k^{n-1} + b)$

where b is such that:

$\displaystyle xb - kb = kx^{n-1} - xk^{n-1}$

But I can't find such a b.

Then I tried to do it by long division of polynomials but because the exponent is n and not a given value, this got very messy and I couldn't get it work.

Can someone help me out?

Many thanks