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5.5 Factoring Special Patterns

5.5 Factoring Special Patterns. 12/12/12. Perfect Squares. 1. 5. 8. 11. 1. 1. 5. 25. 8. 64. 11. 121. 2. 6. 2. 4. 9. 12. 6. 36. 3. 9. 81. 12. 144. 3. 9. 7. 10. 13. 4. 7. 49. 10. 100. 13. 169. 4. 16. Review. Find the product (use FOIL) 1.(x + 2) (x – 2)

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5.5 Factoring Special Patterns

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  1. 5.5 Factoring Special Patterns 12/12/12

  2. Perfect Squares 1 5 8 11 1 1 5 25 8 64 11 121 2 6 2 4 9 12 6 36 3 9 81 12 144 3 9 7 10 13 4 7 49 10 100 13 169 4 16

  3. Review Find the product (use FOIL) 1.(x + 2) (x – 2) Answer: x2 – 4 2. (x + 5) (x – 5) Answer: x2 – 25 3. (2x – 3) (2x + 3) Answer: 4x2 – 9 What’s the pattern???

  4. Difference of Two Squares Pattern (a + b) (a – b) = a2– b2 In reverse, a2– b2 gives you (a + b) (a – b) Examples: 1. x2 – 4 = x2 – 22 = (x + 2) (x – 2) 2. x2 – 144 =(x + 12) (x – 12) 3. 4x2 – 25 = (2x + 5) (2x – 5)

  5. If you can’t remember that, you can still use the big X method. Ex. x2 – 4 Ex. x2 + 0x– 4 Think of 2 numbers that Multiply to -4 and Add to 0 2 x -2 = -4 2 + -2 = 0 -4 2 -2 0 Answer: (x + 2) (x - 2)

  6. x2 + 0x– 144 Ex. x2 – 144 Think of 2 numbers that Multiply to -144 and Add to 0 12 x -12 = -144 12 + -12 = 0 -144 12 -12 0 Answer: (x + 12) (x - 12)

  7. Factor: 4x2-25 4x2+0x -25 Think of 2 numbers that Multiply to -100 and Add to 0 -10 x 10 = -100 -10 + 10 = 0 4(-25) = -100 2 4 4 2 Simplify like a fraction . ÷ by 2 Simplify like a fraction . ÷ by 2 10 -10 5 -5 0 Answer: (2x - 5) (2x + 5)

  8. Homework WS 5.3-5.5

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