4.3, due Febraury 4

I think I understand what this section is TRYING to say but I'm having a hard time understanding how it's saying it.  I get the most confused when the proof of a theorem just says to adapt the proof of a related theorem for the integers.  As far as I understand, an irreducible polynomial is analogous to a prime number and a reducible polynomial is analogous to a composite number.  I think I understand the concept of an associate of an element but I would like to see more examples of the application of associates.