I found a bunch of these proofs difficult to understand just because they stated to rewrite things from previous sections but I learn much better by having proofs written out with the correct wording instead of flipping back and forth trying to figure out what to change here and there. I think I started becoming especially confused at theorem 4.11. I can't understand how condition 3 means that a polynomial is irreducible. Isn't part 3 saying that it can be factored by two polynomials so therefore it is reducible? The proof didn't really help me understand this any better. The last theorem and proof would be awesome to go through as well because I had a difficult time with that proof in the original section it was introduced.
Like I said previously, I enjoy talking about polynomials and seeing how connected the properties are between them and types of numbers I've studied about all my life. I feel like I never had as much context about polynomials and why they function with arithmetic and have properties that are essentially so similar to all these other sets of numbers. So for this section in particular, I liked finally making the connection that irreducibility is the same as being prime in the integers. That new lens of looking at reducibility helps me understand it better.
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