1. WHAT IS FACTORING? Writing an expression as a product of it’s factors
The reverse process of multiplying an expression

2. Different ways of Factoring
Factor out a Greatest Common Factor
Factor a polynomial with 4 terms by grouping
Factoring Trinomials of the form x² +bx+c
Factoring Trinomials of the for ax² +bx+c
Prime Polynomials
Other Polynomials and source information

3. Factoring out the GCF Step 1: Identify the GCF
Note: The GCF is the largest monomial that is factor of each term of the polynomial
Step 1: Identify the GCF
Step 2: Divide the GCF out of every term

4. Factoring out the GCF Example 1: 8(y)^7-4(y)^5+2(y)^4
Step 1: Pick out GCF
GCF= 2(y)^4
Step 2: Divide the GCF out of every term
2(y)^4[4(y)^3-2y+1]

5. Factoring out the GCF Example 2: 4(x-2)+x(x-2) Step 1: GCF=(x-2)
Step 2: (x-2)(4+x)

6. Factoring a Polynomial with 4 Terms by Grouping
Note: If you have 4 terms with no GCF try grouping
Step 1: Group the 1st 2 terms and then the last 2 terms
Step2: Factor out GCF from each separate binomial
Step3: Factor out common binomial

7. Factoring a Polynomial with 4 Terms by Grouping
Example: x³+2x²+6x+12
Step 1: (x³+2x²)+(6x+12)
Step 2: x²(x+2) +6(x+2)
Step 3: (x+2)(x²+6)
* Factor out x² from 1st ( )
* Factor out 6 from 2nd ( )
*Divide (x+2) out of both parts

8. Factoring Trinomials that Look Like x²+bx+c
Step 1: Set up ( )( )
Step 2: Find the factors that go in 1st position
For x² it’s always x
Step 3: Find the factors that go in 2nd position
Their product must = c
Their sum must = b
If c’s positive then the factors will have the same sign depending on b
If c’s negative then the factors will be opposite depending on b
Make a chart if needed

9. Factoring Trinomials that Look Like x²+bx+c
Example: a²-6a-16
Step 1: Set up ( )( )
Step 2: (a )(a )
Step 3: Product of factors must = -16
List factors: 1,-16 ; -1,16 ; 2, -8 ; -2,8 ; -4,4 ; 4,-4
Look at your list and see which pairs adds up to -6
You should pick 2,-8
Place those in the 2nd positions
(a+2)(a-8)

10. Factoring Trinomials that Look Like ax²+bx+c where a≠1
Step 1: Set up ( )( )
Step 2: Use trial and error
Factors of a will go in 1st positions
Factors of c will go in 2nd positions

11. Factoring Trinomials that Look Like ax²+bx+c where a≠1
Example: 5x²+8x+3
Step 1: Set up ( )( )
Step 2: Find factors of 5x²
The only factors are 5x and x
Place those in first positions
Find factors of 3
The only factors are 3 and 1
Place those in 2nd positions
Solution: (5x+3)(x+1)

12. Prime Polynomials Like numbers not every polynomial is factorable
These are called Prime Polynomials
You may not realize it’s prime until you start trying to come up with factors
An example would be x²+5x+12
There are no factors of 12 that when added give you 5

13. Other ways to factor Factoring a perfect square trinomial
Factoring a difference of two squares
Factoring a sum of two cubes
Factoring a difference of two cubes
To learn how to do these go to:

14. Sources
Peppard, Kim Peppard. "College Algebra Tutorial on Factoring Polynomials." College Algebra. Juen 22, West Texas A&M University. 24 Sep < /mps/math/mathlab/col_algebra/col_alg _tut7_factor.htm>.