# 6.7 Dividing Polynomials

Dividing polynomials is a process very similar to long division of whole numbers. But before looking at that, first master dividing a polynomial by a monomial. The way to do this is very similar to distributing, but the operation to distribute is the division, dividing each term by the monomial and reducing the resulting expression. This is shown in the following examples.

Example 6.7.1

Divide the following:

1. Breaking this up into fractions, we get:Which yields:
2. Breaking this up into fractions, we get:Which yields:

Long division is required when dividing by more than just a monomial. Long division with polynomials is similar to long division with whole numbers.

Example 6.7.2

Divide the polynomial by

The steps to get this result are as follows:

1. Divide by yielding Multiply by , yielding Subtract and bring down the next term and repeat.
2. Divide by yielding Multiply by yielding Subtract and bring down the next term and repeat.
3. Divide by yielding . Multiply by yielding Subtract.

The solution can be written as either or

The more formal way of writing this answer is the second option.

Example 6.7.3

Divide the polynomial by

The steps to get this result are as follows:

1. Divide by yielding Multiply by yielding Subtract and bring down the next term and repeat.
2. Divide by yielding Multiply by yielding Subtract and bring down the next term and repeat.
3. Divide by yielding 25. Multiply by 25, yielding Subtract.

The solution is with no remainder.

# Questions

Solve the following polynomial divisions.