How do I factor (a^7-b^7)?

It says to use the Factor Theorem, but I can't think of how to approach it using the Factor Theorem.

well if you have a = b then you have found a zero of the function. so a-b must be a factor.

Alright, I knew that already.

How does the long division turn out?

Nevermind...

(a-b)(a^6+a^5*b+a^4*b^2+a^3*b^3+a^2*b^4+a*b^5+b^6)

it ugly, synthetic division may be easier.

but what you have here is know as a binomial number that might make it a it easier.