1) The idea of F[x]/p(x) having a root of p(x) is still a little strange to me if we can focus on that in class. This is also probably silly but the way that we can know if something is irreducible is if it has no roots? Even the extension field K that contains the root doesn't make too much sense to me.
2) It is interesting to see that although the rest of fields modulo polynomials has pretty much mirrored the moduli that we studied before, but now for p(x) to be irreducible, there are a lot more characteristics.
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