Section 4.1 due 9/24

I understood Theorem 4.1 until part iv--is it saying that the bi = 0R because the coefficients are equal to 0? I don't really understand part iv.

I like the familiarity of this section. I started learning about polynomials years ago (middle school or high school?). And the rules are still the same. I like dividing polynomials. Although this class is all about abstraction and proving things, which is not what I did with polynomials in high school, I think it is the start of what will be an interesting chapter.