The connection between factors and zeros is, that the factors of a function are the zeros of that equation with the sign flipped. Division allows to use the information we already have and when we factor it we find the zeros of the equation. If we already have some of the factors using division aids us in finding the others zeros. The degree tell us how many zeros there should be so if a function is squared there should be two zeros so it lets us know that there may be more than the easy zeros to find or possibly imaginary ones. Yes and No because if you write one twice you have the lets say 4 you need as in problem 9. Because we need 4 it tell us that one of the factors repeats itself.