How do you find zeros by factoring a function?

Each factor will contribute a zero. f(x) = Ax^2 + Bx + C will take the form of something like f(x) = (x-r1)(x-r2) when you factor it. Now the zeros are the values of x for which f(x) = 0. You know 0 times anything is zero, so consider one factor at a time. (x-r1) will equal zero when x = r1, therefore r1 is a "zero" (or "root") of f(x). Incidentally, f(x) = 0 when x = r1 because 0*(x-r2) = 0 for any value of r2.

To find the second "zero" find the value of x that makes (x-r2) equal zero.

If f(x) = (x+2)(x+3) then the zeros are -2 and -3, because f(-2) = 0 and f(-3) = 0.

So if you can factor a function, you can easily find its zeros. The challenge is actually factoring the function.