Polynomials behave the same way, only now you stop with a "remainder" when the degree is less than the degree of the denominator (as compared to integers, where you stop when the numerator is less than the demoninator.) But it's still the procedure of rewriting a fraction after doing the long division and stopping with a remainder. It's analogous to converting a simple fraction into a mixed fraction.
So what you need to do is polynomial long division. Do you know how to do that?