You may want to review polynomials, especially adding, subtracting and multiplying them, first.
Dividing polynomials involves four steps. You cycle around these four steps until you have your answer. First, we need to learn some words. The first polynomial is the dividend and the second is the divisor. Our answer will come in two pieces, a quotient and a remainder. You want to arrange both dividend and your divisor in order of decreasing powers of x (so it looks like x2 + 4x −12). Our example will be to divide x4 + 2x3 − x − 2 by x2 − x.
In fact, the next step will give us a new term of 3x to add to the quotient (so our new quotient will be x2 + 3x) and a new dividend of 3x2 − x − 2. The next step will give us a new term of 3 to add to the quotient (so our new quotient will be x2 + 3x + 3) and a new dividend of 2x − 2. Now we're done, since the degree of 2x − 2 is 0, which is less than 2. Now, the final quotient, x2 + 3x + 3, is the quotient, and the final dividend, 2x − 2, is the remainder. Our final answer is written x2 + 3x + 3 + (2x − 2) / (x2 − x); the last bit on the right is the divisor. On this website, though, I've set everything up for you except for the quotient and the remainder.