When looking at factors and zeros, we used to go through this long trivial process that was riddled with multiple ways you could mess up the final answer. Or just another way it couldn't gone wrong, we could just stop at a certain point because it couldn't factor anymore. But surprise, they found a way to make us factor factors EVEN MORE. Luckily, this method makes a lot more sense, and it's not as easy to mess up if you follow the rules. I don't quite get why dividing polynomials makes it easier to factor but it really does. I'm going to go on a limb and say that it's probably due to the fact that you're removing parts of the polynomial one factor at a time therefore you get to a more simplistic version of the original polynomial.
The degree of the polynomial tells us how many zeros it has. Real, imaginary, or repeated (Basically any special circumstance) a polynomial's degree will always tell us how many factors it has but it doesn't say how many unique zeroes it has.
The degree of the polynomial tells us how many zeros it has. Real, imaginary, or repeated (Basically any special circumstance) a polynomial's degree will always tell us how many factors it has but it doesn't say how many unique zeroes it has.