1. 1 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 1.Obtain the grouping number ac. 2.Find the two numbers whose product is the grouping number and whose sum is b. 3.Use those numbers to write bx as the sum of two terms. 4.Factor by grouping. 5.Multiply to check. Grouping Method for Factoring Trinomials of the Form ax 2 + bx + c.

2. 2 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. 2x 2 + 9x + 4 1. The grouping number is 2(4) = 8. 2. The factors of 8 are 1(8) and (2)(4). We choose 1 and 8 because their product is 8 and sum is 9. 3. We write 9x as the sum x + 8x. 4. Factor by grouping. 2x 2 + 9x + 4 = 2x 2 + x + 8x + 4 = x(2x + 1) + 4(2x + 1) = (2x + 1)(x + 4)

3. 3 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. 8x 2 + 10x  3 1. The grouping number is (8)(  3) =  24. 2. We want two numbers whose product is  24 and whose sum is 10. They are 12 and  2. 3. We write 10x as the sum 12x  2x. 4. Factor by grouping. 8x 2 + 10x  3 = 8x 2 + 12x  2x  3 = 4x(2x + 3)  1(2x + 3) = (2x + 3)(4x  1)

4. 4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. 9x 2 + 3x  30 Remove the greatest common factor. 9x 2 + 3x  30 = 3(3x 2 + x – 10) = 3(3x – 5)(x + 2)