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Agenda: Factoring Sum and Difference of Cubes Factor Relays Homework

Factoring Sum and Difference of Cubes “Patterns” 𝑎 3 + 𝑏 3 =(𝑎+𝑏)( 𝑎 2 −𝑎𝑏+ 𝑏 2 ) 𝑎 3 − 𝑏 3 =(𝑎−𝑏)( 𝑎 2 +𝑎𝑏+ 𝑏 2 ) Remember signs: same-different-positive

1. 𝑥 3 +125 A = x b =5 2. 𝑥 3 −27 A = x b =3 𝑎 3 + 𝑏 3 𝑎 3 − 𝑏 3 (𝑥) 3 + (5) 3 (𝑥) 3 − (3) 3 (𝑎+𝑏)(𝑎 2 −𝑎𝑏+ 𝑏 2 ) (𝑎−𝑏)(𝑎 2 +𝑎𝑏+ 𝑏 2 ) (𝑥+5)(𝑥 2 −5𝑥+25) (𝑥−3)(𝑥 2 +3𝑥+9)

3. 8 𝑥 3 +343 A = 2x b =7 4. 64 𝑥 4 −27𝑥 A = 4x b =3 𝑎 3 + 𝑏 3 x(64 𝑥 3 −27) (2𝑥) 3 + (7) 3 𝑥(𝑎 3 − 𝑏 3 ) (𝑎+𝑏)(𝑎 2 −𝑎𝑏+ 𝑏 2 ) 𝑥((4𝑥) 3 − 3 3 ) (2𝑥+7)((2𝑥) 2 −14𝑥+49) 𝑥(𝑎−𝑏)(𝑎 2 +𝑎𝑏+ 𝑏 2 ) (2𝑥+7)(4𝑥 2 −14𝑥+49) x (4𝑥−3)(16𝑥 2 +12𝑥+9)

Other Cubics by Grouping 5. 12𝑥 3 − 9𝑥 2 +4𝑥 −3 6. 2𝑥 3 + 5𝑥 2 +6𝑥+15 3𝑥 2 (4𝑥 −3) +1(4𝑥 −3) 𝑥 2 (2𝑥+5) +3(2𝑥+5) (3 𝑥 2 +1)(4𝑥 −3) ( 𝑥 2 +3)(2𝑥+5) 7. 10𝑝 3 − 20𝑝 2 +6𝑛 −12 2( 5𝑝 3 − 10𝑝 2 +3𝑛 −6) 5𝑝 2 (𝑝−2) +3(𝑝−2) 2( 5𝑝 2 +3)(𝑝−2)

Factor Relays Directions: Get into groups of 4 As a new questions appears you have a new spokesperson for the group Work as a team to get the answer Spokesperson runs up to the board and writes their answer (make sure to keep it covered If your team gets it right, you get one point

5 𝑥 2 +5𝑥 −10 5(𝑥+2)(𝑥−1)

2 𝑛 3 − 𝑛 2 +2𝑛 −1 (2𝑥−1)( 𝑥 2 +1)

18 𝑥 2 −2 2(3𝑥−1)(3𝑥+1)

2 𝑑 2 +12𝑑 −16 2( 𝑑 2 +6𝑑−8)

125 𝑥 3 −216 (5𝑥−6)(25 𝑥 2 +30𝑥+36)

− 𝑣 2 +2𝑣 −1 − (𝑣−1) 2

𝑥 3 +64 (𝑥+4)( 𝑥 2 −4𝑥+16)

5 𝑝 2 +4𝑝 −12 (5𝑥−6)(𝑥+2)

𝑣 3 − 4𝑣 2 +4𝑣 −16 (𝑥−4)( 𝑥 2 +4)

2 𝑎 7 −32 𝑥 3 2 𝑥 3 (𝑥+2)(𝑥−2)( 𝑥 2 +4)

25 𝑥 2 −10𝑥+1 (5𝑥−1) 2

𝑥 4 −10 𝑥 2 +16 ( 𝑥 2 +2)( 𝑥 2 +8)

6 𝑦 3 +21 𝑦 2 +15𝑥 3𝑥(𝑥+1)(2𝑥+5)