4. Divide

Divide the first term in the divisor into the first term in the

dividend. This gives us the first term in the quotient.

Multiply this term in the quotient by the divisor, and subtract

the product from the dividend

When you subtract, remember that subtraction means changing

the sign and adding

Theoretically, you could bring down all the terms from the

divisor into the remainder, but, as we shall see, the next term is the

only one which will come into play at the next step.

Repeat this process with the remainder. Divide the first term in

the divisor into the first term in the remainder. That gives us the

next term in the quotient.

Multiply this next term in the quotient by the divisor, and

subtract from the remainder.

Again, subtract means change the sign and add. When we bring

down the next term it is the last term in the dividend.

Repeat the process again. We can repeat it once more because

there is something you can multiply the first term in the divisor, the

x, by to get the first term in the remainder, the 3x, namely, 3. That is

the next term in the quotient.

We finally get a remainder that has smaller degree than the

divisor. At this point we stop with this quotient and remainder. We

could express our answer as

It is very common to form a fraction by putting the remainder

over the divisor and adding the fraction to the quotient.

These problems can be checked by multiplying the quotient by

the divisor.

and adding the quotient

Notice the relation between the multiplication and division

problems