**Learning Objectives**

After completing this tutorial, you should be able to:

- Write a polynomial equation in standard form.
- Use the zero factor property.
- Solve polynomial equations by factoring.

** Introduction**

In this tutorial we will be putting our factoring skills to the test
again. We will be looking at solving polynomial equations, which
include quadratic equations, by factoring. After completing
this tutorial, you will be a master at solving polynomial equations.
Solving equations in general is a very essential part of algebra.
So I guess we better get to it.

** Tutorial**

If you need a review on polynomials, feel free to go to **Tutorial
6: Polynomials**.

The following is an example of a polynomial equation:

**Standard Form of a Polynomial
Equation**

The following is an example of a polynomial equation in standard form:

A **quadratic equation** is a special type of polynomial equation,
one where the polynomial is of degree 2. If you need a review on
quadratic equations feel free to go to **Tutorial
17: Quadratic Equations**.

Recall that a quadratic equation in standard form looks like this: .

**Solving Polynomial Equations by Factoring**

**Step 1: Simplify each
side if needed.**

This would involve things like removing ( ), removing fractions, adding
like terms, etc.

**To remove ( ): ** Just use the distributive property.

**To remove fractions:** Since fractions are another way to write
division, and the inverse of divide is to multiply, you remove fractions
by multiplying both sides by the LCD of all of your fractions.

**Step 2**: **Write in
standard form, ,
if needed.**

If it is not in standard form, move any term(s) to the appropriate
side by using the addition/subtraction property of equality.

Also, make sure that it is written in descending order by degrees of the terms.

**Step 3**: **Factor.**

If you need a review on factoring go to **Tutorial
7: Factoring Polynomials**.

Step 4: Use the
Zero-Product Principle.

**If ab = 0, then a = 0 or b = 0**.

**0 is our magic number because the only way a product can become 0
is if at least one of it's factors is 0. **

You can not guarantee what the factors would have to be if the product
was set equal to any other number. For example if *ab* = 1, then *a* = 5 and *b* = 1/5 or *a* = 3 and *b* = 1/3, etc. But with the product set equal to 0, we can guarantee
finding the solution by setting each factor equal to 0. That is why
it is important to get it in standard form to begin with.

Step 5: Solve for the equation(s) set up in step 4.

**Example
1**: Solve by factoring.

This polynomial equation is already simplified.

This polynomial equation is already in standard form.

**AND**

**Step 5: Solve for the
equation(s) set up in step 4. **

***Set 2nd factor = 0 and solve**

**Example
2**: Solve by factoring.

This polynomial equation is already simplified.

***Poly. eq. in standard form**

**AND**

**Step 5: Solve for the
equation(s) set up in step 4. **

***Set 2nd factor = 0 and solve**

***Set 3rd factor = 0 and solve**

**Example
3**: Solve by factoring.

This polynomial equation is already simplified.

***Poly. eq. in standard form**

**AND**

**Step 5: Solve for the
equation(s) set up in step 4. **

***Set 3rd factor = 0 and solve**

** 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:Solve each polynomial equation by factoring.

** Need Extra Help on these Topics?**

**http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/****int_alg_tut30_eqfact.htm**

This webpage helps you with solving polynomial equations by factoring.

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

Videos at this site were created and produced by Kim Seward and Virginia Williams Trice.

Last revised on Dec. 16, 2009 by Kim Seward.

All contents copyright (C) 2002 - 2010, WTAMU and Kim Seward.
All rights reserved.