5.3, due on October 14

1. I didn't understand at first why Corollary 5.12 holds for polynomials that are the products of nonlinear irreducible polynomials, but then I read the proof again more carefully and understood it the second time.

2. I thought it was really interesting that for every polynomial p(x) over a field, there is an extension field where p(x) has a root.  It was also really cool to see the definition of the complex numbers in terms of the extension field modulo x^2 + 1.  That was something I had never considered before.