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 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

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 a will go in 1st positions Factors of c 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>.