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Welcome to Factoring

Welcome to Factoring. Back to Basics Multiplication, Addition, Division. Start with the simple stuff. What is 6 x 7? 42 What is 6 + 7 13 Very good. More simple stuff. What is 3 x 5? 15 What is 3 + 5? 8 See how simple!. One more simple one. What is -3 x 4? -12 What is -3 + 4 1

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Welcome to Factoring

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  1. Welcome to Factoring Back to Basics Multiplication, Addition, Division

  2. Start with the simple stuff • What is 6 x 7? • 42 • What is 6 + 7 • 13 Very good

  3. More simple stuff • What is 3 x 5? • 15 • What is 3 + 5? • 8 See how simple!

  4. One more simple one • What is -3 x 4? • -12 • What is -3 + 4 • 1 Good job!

  5. Now lets go in reverse • What are 2 numbers that multiple to 10 and add to 7? • Start with finding all the multiples of 10 • 1 x 10, 2 x 5…… • Do any of those pairs also add up to 7? YES 5 and 2!

  6. Another one • Find 2 numbers that multiply to get 20 and add to get 9 • Multiples of 20? 1 x 20, 2 x 10, 4 x 5….. Any of those pairs add to get 9? 4 and 5

  7. One final one • Find 2 numbers that multiply to get -6 but add to get +1 • List all the multiples of -6 -1 X 6, 1 x -6, -2 x 3, -3 x 2… And the winner is…. -2 and 3

  8. Steps for Factoring • Is the quadratic in standard form? • List a, b, and c • Multiply a x c • Find all the multiples of • Find the pair that also adds to b • Make 2 sets of parentheses with an x in each one ( x )(x ) • Put your multiples of in each • Divide by a • Kick back

  9. Put it into practice Factor x² + 10x + 25 = 0 • 1 b. 10 c. 25 1 x 25 = 25 1 x 25, 5 x 5 Is it in standard form? List a. b. and c. Multiply a x c List the multiples of 25

  10. Continue x² + 10x + 25 = 0 5 and 5 (x ) (x ) (x + 5)(x + 5) DONE Which multiples also add to 10? Put 2 sets of parentheses with x’s in each Put your multiples in each Divide each multiple by a, if they divide nicely, leave alone

  11. Another example • 2x² + 9x + 10 = 0 a.2 b. 9 c. 10 2 x 10 = 20 1x20, 2x10, 4x5…… Is it in standard form? Find a. b. c. Multiply a x c List multiples of 20 Which set of multiples adds to 9?

  12. 4 + 5 = 9 (x )( x ) (x + 4)(x + 5) (x + 4)(x + 5) 2 2 (x + 2)(2x + 5) Put 2 sets of parentheses with x’s in each Put the multiples in each parentheses Divide each number by a Does 4 divide by 2? Does 5 divide by 2? Kickback

  13. Let’s practice • 2x² -7x + 5 = 0 a.2 b.-7 c. 5 2 x 5 = 10 -2 x -5 = 10 and -2 + -5 = -7 (x – 2) (x – 5) (x – 1)(2x – 5)

  14. Another?

  15. Answersto Day 1 Factoring Practice • (x + 5)(x +5) • (5x+2)(x+1) • (x – 8 )(x -3) • (x +4)(x+ 4) OR (x+4)² 5. (x – 1)(2x – 5)

  16. Answers 6. (x – 3)(5x-1) 7. (3x -3)(3x-3) OR (x-1)(x-1) 8. (x -4)(5x-1) 9. (4x + 10)(4x+10) OR (2x+5)(2x+5) 10. (x – 1)(6x -14) 11. (x+6)(3x+1) 12. (4x+10)(x+3)

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