The most difficult part of this section for me was following the proof of the Division Algorithm in F[x]. The subscripts and different notation was a little hard for me to follow. The whole concept of P containing an element of x that is not in R, yet with properties related to R is a little confusing. I guess I don't really understand why this idea is necessary in order to define a polynomial.
The most interesting part of this material for me was now much it reminded me of my Differential Equations class with leading coefficients and degrees and such. I also thought it was interesting when they started talking about x being a specific element of the ring P, and not a variable that can be assigned values. It was also interesting to note how closely the Division Algorithm in F[x] relates to the previous Division Algorithm that we learned.
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