1. 3.3 SPECIAL Factoring 12/5/2012

2. Perfect Squares 11 1 42 2 93 3 164 4 255 5 366 6 49 7 7 648 8 819 9 100 10 121 11 144 12 169 13

3. Review Find the product using FOIL 1.(x + 2) (x – 2) Answer: x 2 – 4 2. (x + 5) (x – 5) Answer: x 2 – 25 3. (2x – 3) (2x + 3) Answer: 4x 2 – 9 What’s the pattern???

4. Difference of Two Squares Pattern (a + b) (a – b) = a 2 – b 2 In reverse, a 2 – b 2 gives you (a + b) (a – b) Examples: 1. x 2 – 4 = x 2 – 2 2 = (x + 2) (x – 2) 2. x 2 – 144 =(x + 12) (x – 12) 3. 4x 2 – 25 = (2x + 5) (2x – 5)

5. 1000 = 10 3 729 = 9 3 512 = 8 3 343 = 7 3 216 = 6 3 Perfect Cubes 125 = 5 3 64 = 4 3 27 = 3 3 8 = 2 3 1 = 1 3

6. The sum of two cubes: The difference of two cubes:

7. Factor the Sum or Difference of Two Cubes a.Factor. x 3x 3 +64 b.Factor. 8p 38p 3 – q 3q 3 SOLUTION Write as sum of two cubes. x 3x 3 +64 = x 3x 3 +4343 a. () 4x + () x 2x 2 4x4x+ – 4242 = Use special product pattern. () 4x + () x 2x 2 4x4x+ – 16 = Simplify.

8. Factor the Sum or Difference of Two Cubes = – () q2p2p + q2q2 2pq+ 4p24p2 () Simplify. b. 8p 38p 3 – q 3q 3 – () 2p 3 q 3q 3 = Write as difference of two cubes. = – () q2p2p + q2q2 2pq2pq [] () 2p 2 + Use special product pattern.

9. Checkpoint Factor the polynomial. 1. x 3x 3 +1 2. 125x 3 +8 ANSWER () 1x + () x 2x 2 x+ – 1 () 25x5x + () 25x 2 10x+ – 4 3. x 3x 3 216 – () 6x + () x 2x 2 6x6x+36 –

10. Factor Polynomials with GCF a. Factor 16x 4 2x.2x. – Take out GCF. = () 2x2x 8x 38x 3 1 – a. 16x 4 2x2x – Use a 3 –b 3 pattern. = () 2x2x 2x2x 1 – 4x 24x 2 2x2x1 ++ ()

11. Factor by Grouping Factor the polynomial. b.a. x 2x 2 () 1x – () 1x – 9 – x 3x 3 2x 22x 2 16x –– 32 + SOLUTION Use distributive property. a. x 2x 2 () 1x – () 1x – 9 – = () 9x 2x 2 – () 1x – Difference of two squares = () 3x – () 3x+ () 1x –

12. Factor by Grouping Factor each group. = ) x 2x 2 – ( – 2 + 16 ( x )) – 2 ( x Use distributive property. = ) – 16 () – 2 ( xx 2x 2 Difference of two squares = () 4x – () 4x+ () 2x – Group terms. b. = () x 3x 3 – () 32 – x 3x 3 2x 22x 2 16x –– 32 + 2x 22x 2 + 16x +

13. Checkpoint Factor the polynomial by grouping. 8. Factor by Grouping x 2x 2 () 6x+ () 6x+4 – 9. x 3x 3 4x 24x 2 25x –– 100 + 10. x 3x 3 3x 23x 2 4x4x12 +++ ANSWERS () 2x – () 2x+ () 6x+ () 5x – () 5x+ () 4x – () 3x+ () 4x 2x 2 +

14. Homework: Worksheet 3.3