2. Aim: Factoring Course: Adv. Alg. & Trig. Aim: Renewing an old friendship some more – factoring, Algebra! Again! Do Now: Factor:2m 2 a + 4m 3 b - 2m 4 c 4x 2 – 25 a 2 – 8a + 7 2x 2 + 5x + 3 3x 2 - 6x - 24

3. Aim: Factoring Course: Adv. Alg. & Trig. Factoring: Greatest Common Factor Factor by finding the greatest common factor: 2m 2 a + 4m 3 b - 2m 4 c 2m 2 (a + 2mb - m 2 c) GCF - 2m 2 General Rules for Factoring with GCF Find the greatest common monomial that is a factor of each term by: finding the greatest common factor of the coefficients finding the greatest common factor for each of the variables Write the original expression as the product of the greatest common factor and the remaining polynomial 3 y2y2 3 y2y2 GCF 3 y2y2 (1 – 3y)=Factor: 3y 2 – 9y 3

4. Aim: Factoring Course: Adv. Alg. & Trig. Factoring: Difference between Perfect Squares - 4x24x2 25 +- 2x2x2x2x55 - x2x2 a2a2 +- 1. Are both terms perfect squares? 2. Are they subtracted? xxa a If yes, then in general terms: x 2 - a 2 = (x - a)(x + a)

5. Aim: Factoring Course: Adv. Alg. & Trig. Factoring Trinomials a = 1 ( )( ) FL a 2 - 8a + 7 aa71 -- O -7a + I -1a -8a

6. Aim: Factoring Course: Adv. Alg. & Trig. Factoring Trinomials a  1 Factor: 2x 2 + 5x + 3 What do you know? 1. The product of 2 binomials ( )( ) 2. 1st Terms (2x )(x ) 3. Last Terms ( 1)( 3) 4. Signs ( + )( + ) Possible Combinations: (2x + 1)(x + 3) or (2x + 3)(x + 1) 1x1x 6x6x 7x7x 3x3x 2x2x 5x5x 5x = sum of O & I O

7. Aim: Factoring Course: Adv. Alg. & Trig. Factor Completely 3x 2 - 6x - 24 3(x 2 - 2x - 8) 3(x - 4)(x + 2) 1. Find the GCF 2. Factor the trinomial

8. Aim: Factoring Course: Adv. Alg. & Trig. Factoring - Perfect Cubes Factoring Difference/Sum of Perfect Cubes u 3 – v 3 = (u – v)(u 2 + uv + v 2 ) u 3 + v 3 = (u + v)(u 2 – uv + v 2 ) Factor: x 3 – 27 x 9 + 125 x 3 and -27 are perfect cubes: -27 = (-3) 3 u = x and v = (-3) = (x – (-3)) (x 2 + x(-3) + (-3) 2 ) = (x + 3)(x 2 – 3x + 9) x 9 and 125 are perfect cubes: x 9 = (x 3 ) 3 125 = 5 3 = (x 3 + 5) ((x 3 ) 2 – x 3 (5) + 5 2 ) = (x 3 + 5)(x 6 – 5x 3 + 25) u = x 3 and v = 5

9. Aim: Factoring Course: Adv. Alg. & Trig. Model Problems 1.144 - d 2 2. 9x 2 - 16y 2 3. x 4 - y 6 4. 8x 2 - 8y 2 (12 - d)(12 + d) (9x - 4y)(9x + 4y) (x 2 - y 3 )(x 2 + y 3 ) 8(x - y)(x + y) 8(x 2 - y 2 ) 5. s 8 - t 4 (s 4 - t 2 )(s 4 + t 2 ) (s 2 - t)(s 2 + t)(s 4 + t 2 ) Note: Check your factoring by multiplying the factors to come up with the original expression. G.C.F.

10. Aim: Factoring Course: Adv. Alg. & Trig. Model Problems Factor Completely 1.4a 2 + a – 3 2.8m 3 - 1 3.r 3 + 3r 2 – 54r 4.4x 6 – 4x 2 5.5y 5 + 135y 2