2. Use long division to get a quotient and a remainder.

Divide the first term in the divisor into the first term in the
dividend. *x* goes into 2*x*^{3} 2*x*^{2} times. This is the first term in the
quotient.

Multiply this term in the quotient by the divisor and subtract from the dividend.

Repeat the process with the remainder. Divide the first term in
the quotient into the first term in the remainder. *x* goes into -3*x* -3
times. Put -3 in the next place in the quotient. Then multiply this term in the quotient times the divisor and subtract
from the remainder.

Remember that subtract means change the sign and add.

At this point, the remainder has smaller degree than the divisor, so we stop and put the remainder over the divisor and add the fraction to the quotient,

or, more simply,

Before checking our work, it will be avantageous to develop terminology for the characters in this drama

The expression you are dividing into is the dividend. The expression which we are dividing by is the dividend. The result, which goes above the box, is called the quotient, and the remainder is the difference at the bottom of the problem. The way it works is

The answer to a division problem is what you need to miultiply the divisor by to get the dividend. If we multiply the divisor by the answer,

we should distribute this out.

= 2*x*^{3} - 4*x*^{2} - 3*x* + 6 - 4

= 2*x*^{3} - 4*x*^{2} - 3*x* + 2

which is the dividend.

This illustrates that to check a long division problem, mutiply the divisor by the quotient and add the remainder to the product. This should equal the dividend.