3. Factoring Polynomials First: Look for a GCF 4 Second: Number of Terms 2 3 Cubes Squares Perfect Square Trinomial Grouping X 2 – 9 X 3 – 27 = (x - 3) (x 2 + 3 x + 9) = (x - 3) (x + 3) X 2 + 8x + 12= (x + 6) (x + 2) X 2 + 14 x + 49 = (x + 7) 2 X 3 – 3 x 2 + 9x - 27 = x 2 (x - 3) + 9 (x -3) = (x - 3) + (x 2 +9)

4. 12 X 3 + 8 x 2 y 2 X 3 -6 x 2 + 12x 15 X 5 + 20x 3 49 a 3 – 35 a = 4x 2 (3x +2y) Factorize: = 7a (7a 2 - 5) = 5x 3 ( 3x 2 + 4) = 2x (x 2 – 3x + 6) H.C.F.

5. X 2 – 9 X 2 – 100 4X 2 – 25 X 2 – 49 50 X 2 – 18 = (x - 3) (x + 3) Factorize: = 2(25x 2 - 9) = 2(5x – 3)(5x + 3) = (x-7) (x+7) = (2x-5) (2x+5) = (x-10) (x + 10)

7. X 3 – 27 X 3 – 1000 8X 3 + 125 X 3 + 343 16 X 5 – 54 x 2 = (x - 3) (x 2 + 3 x + 9) Factorize: = 2x 2 (8x 3 - 27) = 2x 2 (2x – 3)(4x 2 + 6x + 9) = (x+7) ( x 2 – 7x +49 ) =(2x+5) (4 x 2 – 10x + 25) = (x-10) (x 2 + 10x + 100)

9. X 2 + 8x + 12 X 2 -11x + 24 X 2 + 10x -24 X 2 - 35x - 36 = (x +6) (x + 2) Factorize: = (x- 36) (x+1) = ( x+12) ( x-2) = (x- 8) (x - 3) Trinomials