#
Section 7-3

#
Dividing Polynomials

To
divide one polynomial by another
, first try writing it as a rational expression
and finding common factors. If you can't find a common factor, then use polynomial
long division.

Example 1:

Divide.

Write as a rational expression, and factor the numerator.

Cancel the common factor.

**
**

Example 2:

Divide.

We can factor the dividend as (
*
m
*
+ 6)(
*
m
*
– 2), but that
doesn't help us in this case. Instead, we'll use long division.

Write using the long division symbol. Divide the leading terms,
*
m
*
^{
2
}
÷
*
m.
*

Multiply and subtract.

Bring down the –12. Again, divide the leading terms,
*
m
*
÷
*
m.
*

Multiply and subtract.

Write the quotient with remainder.