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 + 2x3x − 2 by x2x.

  1. Divide. This means you divide the first term of the dividend by the first term of the divisor. In this case, we divide x4 by x2. We get x2. We add this to our quotient. Since we don't have a quotient yet, this becomes the first piece, so our temporary quotient is x2.
  2. Multiply. This means you multiply the answer you got in the last step by the whole divisor. In this case, we multiply x2 by x2x. We get x4x3.
  3. Subtract. This means you subtract the answer you got in the last step from the whole dividend. In this case, we subtract x4x3 from x4 + 2x3x − 2. Remember that that means (x4 + 2x3x − 2) − (x4x3), so we get 3x3x − 2. This is our new dividend; you can forget about the old one for the rest of the problem.
  4. Check if you're done. You're done if the degree of the dividend (the new dividend) is less than the degree of the divisor. In this case, the new dividend still has degree 3, while the divisor has degree 2, so we're not done yet.

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 3x2x − 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) / (x2x); 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.