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 *x*^{2} +
4*x* −12). Our example will be to
divide *x*^{4} + 2*x*^{3}
− *x* − 2 by *x*^{2}
− *x*.

- Divide. This means you divide the first term of the dividend
by the first term of the divisor. In this case, we
divide
*x*^{4}by*x*^{2}. We get*x*^{2}. We add this to our quotient. Since we don't have a quotient yet, this becomes the first piece, so our temporary quotient is*x*^{2}. - Multiply. This means you multiply the answer you got in the
last step by the
*whole*divisor. In this case, we multiply*x*^{2}by*x*^{2}−*x*. We get*x*^{4}−*x*^{3}. - Subtract. This means you subtract the answer you got in the
last step from the
*whole*dividend. In this case, we subtract*x*^{4}−*x*^{3}from*x*^{4}+ 2*x*^{3}−*x*− 2. Remember that that means (*x*^{4}+ 2*x*^{3}−*x*− 2) − (*x*^{4}−*x*^{3}), so we get 3*x*^{3}−*x*− 2. This is our new dividend; you can forget about the old one for the rest of the problem. - 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 3*x* to
add to the quotient (so our new quotient will
be *x*^{2} + 3*x*) and a new dividend of
3*x*^{2} − *x* − 2. The next step
will give us a new term of 3 to add to the quotient (so our new
quotient will be *x*^{2} + 3*x* + 3) and a new
dividend of 2*x* − 2. Now we're done, since the degree
of 2*x* − 2 is 0, which is less than 2. Now, the final
quotient, *x*^{2} + 3*x* + 3, is the quotient,
and the final dividend, 2*x* − 2, is the remainder. Our
final answer is written *x*^{2} + 3*x* + 3 +
(2*x* − 2) / (*x*^{2} − *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.