4.2, due on February 2

1. I am not sure how if f(x) divides g(x), then cf(x) also divides g(x) for each nonzero c in the field F, and how this statement shows that a nonzero polynomial may have infinitely many divisors... How can a polynomial have such a property?

2. The section was so cool - you could use the Division Algorithm on polynomials! This property as well as others like Thoerem 4.5 and 4.6 related directly to sections about divisibility in the beginning of the book. Thus, it was easier to grasp these slightly more difficult concepts with polynomials.