The 7 Forms of Factoring


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	Finding the Greatest Common Factor (GCF)
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A. Introduction:

Factoring is perhaps the most important skill you will needfor much of Beginning Algebra, Intermediate Algebra, and evenCollege Algebra and Finite Math. Let's look briefly at what itmeans to factor.

B. The Meaning of "to factor."

"To factor" means, "to rewrite as a product(things being multiplied)."

For instance, if we were to rewrite 12 as 9 + 3, we would berewriting it as a SUM (things being added, or as terms).

However, if we choose to rewrite 12 as 3 * 4, we would berewriting it as a PRODUCT (things being multiplied).

Then, we could make the following observations:

1. We factored the 12 as 3 * 4.

2. And, 3 and 4 are factors of 12.

C. Why Do We Factor?

There are a number of reasons why we factor but perhaps thetwo most important are:

1. We factor in order to simplify or reduce algebraicexpressions so they are simpler and easier to work with.

2. We also factor in order that we may rewrite an equation soit fits the ZEROFACTOR PROPERTY. The Zero- Factor Property, verysimply put, says that if the product of two "things" iszero, then one or both of the "things" must be zero.This allows us to set each of the "things" equal tozero and to solve equations we were not able to previously solve.

D. How to Master Factoring

As a warning, if you don't master it quickly, you will fallbehind in understanding and applying new skills and conceptssince so many of them will involve factoring. I suggest thefollowing approach:

1. Memorize the names of the 7 Forms of Factoring given on thenext page.

2. Notice how the name of each describes the structure orappearance of the next factoring form.

3. Think of each of the 7 Factoring Forms as a separate"room" in the larger "house" of Factoring.

4. In order to factor, we us a different procedure in eachroom. When you know which room you're in, then you can know whatto do. This approach of giving attention to the names andaccompanying structures is critical for success in your long-range math goals of completing the core requirement.

E. The 7 Forms of Factoring

Always	1. Greatest Common Factor (G. C. F.) 2. Difference of Two Squares
2 Terms	3. Difference of Two Cubes 4. Sum of Two Cubes
3 Terms	5. Perfect Square Trinomial 6. A Quadratic Trinomial
4 Terms	7. Factor by Grouping

Note: As you factor, you will be following acertain pattern: Always check for the Greatest Common Factor, anddo that first. Then, look at what remains.

Is it Two Terms? Then look to see if it fits the structure of #2, #3, or #4 above.
Is it Three Terms? See if it fits the structure of #5 or #6.
Is it Four Terms? Then it may be #7, Factor by Grouping.