1. The hardest thing for me is probably keeping straight the actual polynomial and the function induced by the polynomial, especially when both use the same symbol. The paragraph on true and false statements in particular took a little while to wrap my brain around.
2. It was really interesting to see concepts from high school algebra showing up in an abstract algebra class. Corollary 4.16 is one good example of this; it's a generalization of the same theorem about roots of polynomials in R.
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