**Learning Objectives**

After completing this tutorial, you should be able to:

- Divide a polynomial by a monomial.
- Divide a polynomial by a polynomial 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 Monomial**

If you need a review on the distributive property, go to **Tutorial
8: Properties of Real Numbers.**

**Step 2: Simplify
the fractions.**

If you need a review on simplifying fractions, go to **Tutorial
3: Fractions.**

**AND**

**Step 2: Simplify
the fractions.**

***Simplify each term**

**Divide**

**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.

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 one more time on this problem.

We just follow the the same steps 2 - 4 as shown above. Our "new
divisor" is the last line 8*x* + 1.

We keep going until we can not divide anymore.

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

**AND**

**Step 3 (repeated): Take the
term found in step 1 and multiply it times the divisor.**

**AND**

**Step 4 (repeated): Subtract
this from the line above.**

**2nd term:**

**3rd term:**

**4th term:**

** 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 - 1c:Divide.

** Need Extra Help on these Topics?**

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

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

This webpage helps you with dividing polynomials.

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

This webpage will help you with long division.

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on August 2, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.