Assignment 14: Sections 4.5 - 4.6

Difficult: The most difficult part of these sections for me was understanding the proofs presented in the text. The two most difficult theorems for me to understand were the theorem about the irreducibility of a polynomial in Q[x] based on its irreducibility in Z[x] and Einstein's Criterion. It is interesting that they work to find which polynomials are irreducible, but I don't quite understand why.

Reflective: The most interesting section for me was section 4.6. I think the fundamental theorem of algebra is really exciting. I like C[x] and other rings or problems dealing with complex numbers. I think it is very useful that every polynomial in C[x] (except polynomials of degree one) is reducible. This theorem is easy to understand and interesting to consider. Imaginary numbers really do explain a lot of characteristics of polynomials.