1. Something that I struggled with was trying to find all the irreducible polynomials of degree 3 in the integers mod2 WITHOUT writing out all possible options and cancelling out the ones that are reducible. I think there is a way that is simpler, like using associates, but I am not quite sure how that works.
2. What I thought was really cool was that you can apply properties of integers having a unique prime factorization, to what we talked about in this section. In other words, polynomials are reducible (like a prime factorization) if it has divisors other than just its associates (like the prime itself) and the nonzero constant polynomials (like 1). At least I am pretty sure that is the comparison. Knowing this was useful for doing the homework as well.
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