I'm just curious why we factor before finding the zeros of an equation. My guess is that it has something to do with the zero product property.
in the case of a quadratic, factoring IS finding the zeros: if f(a) = 0, then x - a is a factor, and vice versa.
for higher degree polynomial equations, factoring (if possible) reduces the problem to one that is easier to solve.
So, by setting f(x) or y equal to zero. It simply stating where y is equal to zero, you can solve for x to find where x will make y equal zero. Thus, satisfying the definition of an zero or x-intercept. I really have to learn the philosophy of math to get how these statements of equality can exist. Thanks again Devano.