When I read Theorem 4.2, I was pretty confused at first. I'm not sure what I thought it was referring to, but I already know that x^4*x^2=x^6 because you add exponents when you're multiplying them together. I don't think I've ever heard them referred to as "degrees" before, so when I read deg[f(x)g(x)] = deg[f(x)]+deg[g(x)] I was thinking more of regular arithmetic than exponents.
Reflective:
The Division Algorithm In F(x) seems almost exactly the same as the regular division algorithm, but they don't require r(x) to be greater than zero. I didn't totally follow the proof, and perhaps it was addressed in there, but I'm curious as to why r(x) doesn't have to be greater than zero...
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