**Learning Objectives**

After completing this tutorial, you should be able to:

- Divide one polynomial by another using long division.

**Introduction**

In this tutorial we revisit something that you may not have seen since
grade school: long division. In this tutorial we are dividing
polynomials, but it follows the same steps and thought process as when
you apply it numbers. Let's forge ahead.

** Tutorial**

**Polynomial Polynomial**

The divisor (what you are dividing by) goes on the outside of the box.
The dividend (what you are dividing into) goes on the inside of the box.

When you write out the dividend, make sure that you insert 0's for any missing terms. For example, if you had the polynomial , the first term has degree 4, then the next highest degree is 1. It is missing degrees 3 and 2. So if we were to put it inside a division box, we would write it like this:

This will allow you to line up like terms when you go through the problem.

The quotient (answer) is written above the division box.

Make sure that you line up the first term of the quotient with the term
of the dividend that has the same degree.

Make sure that you line up all terms of this step with the term of
the dividend that has the same degree.

Make sure that you subtract EVERY term found in step 3, not just the
first one.

You keep going until the degree of the "new" dividend is less than
the degree of the divisor.

Your answer is the quotient that you ended up with on the top of the
division box.

If you have a remainder, write it over the divisor in your final answer.

We keep going until we can not divide anymore. It looks
like we can go at least one more time on this problem.

We just follow the the same steps 2 - 4 as shown above. Our "new
dividend" is the last line .

We keep going until we can not divide anymore. It looks
like we can go one more time on this problem.

We just follow the the same steps 2 - 4 as shown above. Our "new
dividend" is the last line .

We keep going until we can not divide anymore.

We just follow the the same steps 2 - 4 as shown above. Our "new
dividend" is always going to be the last line that was found in step 4.

**AND**

**AND**

**2nd term:**

**3rd term:**

**Note that each second line is SUBTRACTED, so
the line shows what the signs of each term would be when you subtract it. **

** Practice Problems**

These are practice problems to help bring you to the next level.
It will allow you to check and see if you have an understanding of these
types of problems. **Math works just like anything
else, if you want to get good at it, then you need to practice it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.**
In fact there is no such thing as too much practice.

To get the most out of these, **you should work the problem out on
your own and then check your answer by clicking on the link for the answer/discussion
for that problem**. At the link you will find the answer
as well as any steps that went into finding that answer.

Practice Problems 1a - 1b: Divide using long division.

** Need Extra Help on these Topics?**

**The following are webpages that can assist
you in the topics that were covered on this page:**

This webpage goes over long division.

**http://www.purplemath.com/modules/polydiv.htm**

This webpage goes over long division.

**http://www.sosmath.com/algebra/factor/fac01/fac01.html**

This webpage goes over long division.

Last revised on March 15, 2012 by Kim Seward.

All contents copyright (C) 2002 - 2012, WTAMU and Kim Seward. All rights reserved.