Learning Objectives
Introduction
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.
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.
Also, make sure that it is written in descending order by degrees of the terms.
Step 3: Factor.
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.
AND
Step 5: Solve for the
equation(s) set up in step 4.
*Set 2nd factor = 0 and solve
Example 2: Solve by factoring.
*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.
*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
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.
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