College Algebra
Tutorial 36: Long Division
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
Divide
Polynomial Polynomial
Using Long Division

Step 1: Set up the long
division.
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. 

Step 2: Divide
1st term of dividend by first term of divisor to get first term of the
quotient. 
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. 
Step 3: Take the
term found in step 2 and multiply it times the divisor. 
Make sure that you line up all terms of this step with the term of
the dividend that has the same degree. 
Step 4: Subtract
this from the line above. 
Make sure that you subtract EVERY term found in step 3, not just the
first one. 
Step 5: Repeat
until done. 
You keep going until the degree of the "new" dividend is less than
the degree of the divisor. 
Step 6: Write out the
answer. 
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. 
Example 1: Divide using long division . 

*Write in descending order 
Note that the "scratch work" that you see
at the right of the long division shows you how that step is filled in.
It shows you the "behind the scenes" of how each part comes about. 

Scratch work:

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 . 

*Quotient with no remainder 
Example 2: Divide using long division . 

*Write in descending order
*Insert 0 for missing term 
Note that the "scratch work" that you see
at the right of the long division shows you how that step is filled in.
It shows you the "behind the scenes" of how each part comes about. 
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. 
The following is the scratch work (or behind
the scenes if you will) for the rest of the problem. You
can see everything put together following the scratch work under "putting
it all together". This is just to show you how the different pieces
came about in the final answer. When you work a problem like this,
you don't necessarily have to write it out like this. You can have
it look like the final product shown after this scratch work. 
Scratch work for steps 2, 3 and 4
for the last two terms of the quotient
2nd term:
3rd term:


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


*Quotient with a remainder of 37 
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:

Last revised on March 15, 2012 by Kim Seward.
All contents copyright (C) 2002  2012, WTAMU and Kim Seward. All rights reserved.

