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WHAT IS FACTORING?

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 x ² +bx+c

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WHAT IS FACTORING?

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  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 • 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 outx² 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: • http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm

  14. 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>.

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