4.2 Due February 2

The thing that was most difficult for me was the part about if f(x)|g(x) then cf(x)|g(x). I find this weird because that's definitely not like normal arithmetic. The other thing that bugged me was why the gcd of two polynomials is the highest degree monic polynomial that divides both polynomials. This bugged me a little because of all the potential cf(x)'s that could be greater common divisors. However it makes sense, because we could have an infinite number of divisors and really we just need one to be defined as gcd which can be defined in all cases and the monic polynomial fits that role.

The thing that this reading made me think about is that if we can have relatively prime polynomials, can we have prime polynomials? How about unique prime factorization of polynomials? This is interesting stuff.