I think the most interesting thing was to see specific examples of how integer rules and proofs can be adapted for F[x]. It helps a lot that the definitions, although they seem completely different in many ways, still mean the same things in F[x]. Such as the gcd still being written as a linear combination only now it's of functions instead of just numbers.
The hardest thing for me is knowing how to start the division algorithm to find the gcd of a function. I know how do use long division to divide polynomials, I just get stuck on the starting point. Or maybe it's obvious and I'm just not yet seeing the connection I need to.
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