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