6.4 Factoring Polynomial Equations * OBJ: Factor sum & difference of cubes Do Now: Factor 1) 25x 2 – 492) x 2 + 8x + 16 (5x + 7)(5x – 7) (x + 4)(x + 4)

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6.4 Factoring Polynomial Equations * OBJ: Factor sum & difference of cubes Do Now: Factor 1) 25x 2 – 492) x 2 + 8x + 16 (5x + 7)(5x – 7) (x + 4)(x + 4) (x + 4) 2 Difference of Squares (DOS) Perfect Trinomial Square (PTS)

a3 + b3 = (a + b)(a2 – ab + b2) Factoring Sum of Cubes Ex 1: x (x) 3 + (2) 3 (x + 2)(x 2 – 2x + 4) Ex 2: n (n) 3 + (3) 3 (n + 3)(n 2 – 3n + 9)

Factoring Difference of Cubes a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Ex 3: 8x 3 – 1 (2x) 3 – (1) 3 (2x – 1)((2x) 2 + 2x + (1) 2 ) (2x – 1)(4x 2 + 2x + 1) Ex 4: 125x 3 – 64 (5x) 3 – (4) 3 (5x – 4)((5x) x + (4) 2 ) (5x – 4)(25x x + 16)

Ex 5: x3 – 2x2 – 9x + 18 (x3 – 2x2) + (-9x + 18) Group with a ‘+’ in the middle x2(x – 2) - 9(x – 2) GCF each group (x – 2)(x2 – 9) GCF each group (x – 2)(x + 3)(x – 3) Factor all the way (DOS) Factor by Grouping Factor by Grouping *(when there are more than 3 terms) continued… Do Now: Factor x 2 – 25 = (x+5)(x-5)

Ex 6: 2x3 - 3x2 - 8x + 12 (2x3 - 3x2) + (-8x + 12) x2(2x – 3) - 4(2x - 3) (2x – 3)(x2 – 4) (2x – 3)(x + 2)(x – 2) Ex 7: x3 - 2x x + 32 (x3 - 2x2) + (-16x + 32) x2(x – 2) -16(x - 2) (x – 2)(x2 – 16) (x – 2)(x + 4)(x – 4)

Factoring in Quadratic Form Ex 8: 81x 4 – 16 (9x 2 ) 2 – (4) 2 *DOS (9x 2 + 4)(9x 2 – 4) *DOS again! (9x 2 + 4)(3x + 2)(3x - 2) Ex 9: x 4 – 256 (x 2 ) 2 – (16) 2 (x )(x 2 – 16) (x )(x + 4)(x - 4) Look for DOS pattern

Ex 10: 4x 6 – 20x x 2 4x 2 (x 4 - 5x 2 + 6) 4x 2 (x 4 - 3x 2 - 2x 2 + 6) 4x 2 (x 2 (x 2 – 3) - 2(x 2 – 3)) 4x 2 (x 2 – 3)(x 2 – 2) Look for GCF and Bust da B HW:

continued… Use Factoring to Solve Polynomial Equations Do Now: Solve (x+5)(x-3)(x+3)=0 x+5=0 x–3=0 x+3=0 x = -5 x = 3 x = -3 2y 5 – 18y = 0 2y (y 4 - 9) = 0 2y (y 2 + 3) (y 2 – 3) = 0 y=0y=±i√3 y=±√3 Ex 11:

2x x = 14x 3 2x x x = 0 Put in standard form 2x (x 4 – 7x 2 +12) = 0 GCF 2x (x 4 – 3x 2 – 4x 2 +12) = 0 Bustin’ da B 2x( x 2 (x 2 – 3) - 4(x 2 – 3) ) = 0 2x (x 2 - 3)(x 2 – 4) = 0 2x (x 2 – 3)(x + 2)(x – 2) = 0 Factor everything 2x=0 x 2 -3=0 x+2=0 x-2=0 x=0 x=±√3 x=-2 x=2 Ex 12: HW: