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

2x2 + x + 3   R   10

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.