Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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) * Factor out x² from 1st ( ) * Factor out 6 from 2nd ( ) • Step 3: (x+2)(x²+6) *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/mat hlab/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>.