Section 4.4, due on September 29

The most difficult part of this section was the the idea of a polynomial inducing a function. I have never heard of this before and it is still not super concrete in my mind. I'm not really sure why the concept of a polynomial inducing a function is so important and why it needs to be so distinctly distinguished between polynomial. I also found Corollary 4.19 to be a little hard for me to understand.

The most interesting part of this section was the remainder theorem. I don't think I had ever realized that before and I thought it was really neat. I also thought it was cool that to show that a deg 2 or 3 polynomial is irreducible you need only verify that it has no roots in the field F. It reminded me a lot of high school algebra, but with a cooler twist than they teach you. I feel like I finally am starting to understand the origin behind some of those facts that I just took for granted.