WHAT IS FACTORING?

•Writing an expression as a product of it’s factors•The reverse process of multiplying an expression

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

Factoring out 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

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]

Factoring out the GCF

• Example 2: 4(x-2)+x(x-2)

• Step 1: GCF=(x-2)

• Step 2: (x-2)(4+x)

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

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

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

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)

Factoring Trinomials that Look Like ax²+bx+c where a≠1

• Step 1: Set up ( )( )

• Step 2: Use trial and error– Factors of aa will go in 1st positions– Factors of cc will go in 2nd positions

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)

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

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:– http://www.wtamu.edu/academic/anns/mps/math/

mathlab/col_algebra/col_alg_tut7_factor.htm

Sources

• Peppard, Kim Peppard. "College Algebra Tutorial on Factoring Polynomials."

College Algebra. Juen 22, 2003. West Texas A&M University. 24 Sep 2006 <http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm>.