4.3

1. What was the most difficult part of the reading for you?
Oh my gosh, maybe it was because we had to do homework right after doing some reading for this section with out a class period to digest, but I feel pretty lost. I'm not confused by the idea that something is "irreducible"  or "reducible" but trying to do the homework tonight proved to me that I don't know how to tell for sure when something is irreducible or not. Also, this "associate" thing.... what is that? I don't understand it. I mean, I guess I understand that it is the product of a unit and something else, but I really don't understand much else about it, and that makes me sad.

2. Why I felt lost on the homework
So, I'm specifically talking about 4.3 2 and 9. I really struggled with 2 because I really don't understand associates. I understand being non-zero, I understand monic, and I understand unique. That being said, I don't even understand what I'm being asked to prove in number 2.
For number 9, wow.... Is there an easier way to do this? What I did for parts a) and b) is I wrote down every possible function I could imagine (for part a I wrote down a list of the polynomials with degree 2 in Z(2)) which weren't that many. Then, looking at them, I just eliminated things I knew could be factored. Then, when I remembered I was in Z(2) and should be able to eliminate some more things, I wrote down the two possible factors (x and x+1) and wrote the 3 possible combinations of the two. (x^2, x(x+1), and (x+1)^2) and eliminated those options too, leaving me with the one irreducible thing. Well, I was able to do that for part b, but it took a little more time. Then, realizing that I had to pretty much check 27 different combinations for part c made me tired and I just feel like there must be some easier way to see if things were irreducible or not. I just don't know what it is. Seriously, what am I not getting here.