Difficult: The thing I found most difficult in this section was the idea of an extension field. I don't really get the point of this. So it makes irreducible polynomials have roots in the extension field, but I couldn't figure out what those roots are, or why it matters. I was also didn't understand how the extension field can help us define complex numbers either. Basically, I just don't understand why extension fields are important, and what it helps us do.
Connections: So I feel like I am starting to get the hang of working with polynomials modulo p(x), but it is pretty different from modular arithmetic with integers. I also like that I am getting more practice with irreducible polynomials, and finding them. I like using the root test to find or verify that a polynomial is reducible or irreducible. This is a simpler way for me than trying to find all of the reducible ones and picking one that is not in that list. So it is nice to work more with irreducible polynomials in this section so that I can get more comfortable with them.
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