Factor by Grouping

Polynomials with 1,2, and 3 terms have special names A polynomial is the sum of 1 or more terms Polynomials with 4 terms can be factored by grouping To FACTOR a polynomial is to rewrite it as: Addition Subtraction Multiplication Division The BOX can be used to factor by grouping (4m-2)(m+7) As a warmup, you will place FOIL answers in the BOX 4m -2 -2m 4m ^{2}m 28m -14 7 Multiply the outside terms to find the missing products inside the boxes 2m -5 -5m ? 2m ^{2}? m 12m ? -30 ? +6 Multiply the outside terms to find the missing products inside the boxes 3m -1 -2m ? 6m ^{2}? 2m -6m ? -2 2 ? Select the missing Greatest Common Factors for each row and column 2m ? -5 ? -5m 2m ^{2}m ? -30 12m +6 ? Fill in the missing GCFs for each row and column -4m 6m ^{2}-6 9m 6m ^{2}+9m-4m-6(3m-2)(2m+3) The 4 term polynomial: Factors to Click OK 3m -2 -4m 6m ^{2}2m -6 9m 3 Fill in the missing GCFs for each row and column 6m ^{2}3m 8m 4 (3m+2m)(4+1) (3m-4)(2m-1) (3m+4)(2m+1) 6m ^{2}+8m+3m+4Factors to: The 4 term polynomial: 2m 1 6m ^{2}3m 3m 8m 4 4 How many polynomial terms are needed to factor by grouping? 3 terms 4 terms 5 terms ? ? ? ? Which polynomial can be factored by grouping? a ^{2}-94b ^{2}+6b-2b-32b ^{3}-4b^{2}+6b-2b-3Factor this polynomial by grouping 4b ^{2}+6b-2b-3Fill in the 4b ^{2}-2b -3 6b The 4 term polynomial 4b ^{2}+6b-2b-3(2b-3)(2b-1) (2b3)(2b1) (2b+3)(2b-1) (2b+2b)(3-1) factors to.... 2b -1 4b ^{2}-2b 2b -3 6b 3 |

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