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RULES FOR FACTORING

RULES FOR FACTORING. Step 1: CMF. Step 2: Binomial?. DOTS?. Step 3: Trinomial?. PST?. Guess Method. RULES FOR FACTORING. REVIEW OF CMF. (x 2 – 2). 6x 2 – 12 =. 6. (x 2 – 2x + 6). 3x 2 – 6x + 18 =. 3. (2x 2 + 3x – 1). 10x 3 + 15x 2 – 5x =. 5x. D.O.T.S.

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RULES FOR FACTORING

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  1. RULES FOR FACTORING Step 1: CMF Step 2: Binomial? DOTS? Step 3: Trinomial? PST? Guess Method

  2. RULES FOR FACTORING REVIEW OF CMF (x2 – 2) 6x2 – 12 = 6 (x2 – 2x + 6) 3x2 – 6x + 18 = 3 (2x2 + 3x – 1) 10x3 + 15x2 – 5x = 5x

  3. D.O.T.S. DifferenceOfTwoSquares Perfect Squares Difference means subtract x2 9 9x2 So, examples of DOTS: y2 16 25y2 a2 49 81x2y2 x2 – 16 or 4a2 – 25b2 4x4y6 100 b6

  4. D.O.T.S. FLASH CARDS Is it DOTS? x2 – y2 D

  5. D.O.T.S. FLASH CARDS Is it DOTS? a2 – 9 D

  6. D.O.T.S. FLASH CARDS Is it DOTS? 6m2 – 81 D Why not? 6 IS NOT A PERFECT SQUARE!

  7. D.O.T.S. FLASH CARDS Is it DOTS? 4b2 + 25 D Why not? THIS IS A SUM OF 2 SQUARES.

  8. D.O.T.S. FLASH CARDS Is it DOTS? 49b2 – 100c4 D

  9. D.O.T.S. DifferenceOfTwoSquares DOTS always factors the same way. (Square root of the first + square root of the last) times (Square root of the first – square root of the last) Example: x2 – 16 = (x 4) (x – 4) +

  10. D.O.T.S. DifferenceOfTwoSquares 4a2 – 25b2 = (2a + 5b) (2a – 5b) b2 – 49 = (b + 7) (b – 7) (3xy – 8b3) 9x2y2 – 64b6 = (3xy + 8b3)

  11. ? P.S.T. Perfect Square Trinomial How to identify: ☺1st & last term must be perfect squares YES! x2 + 6x + 9 ☺Square root of the first ☺Square root of the last x 3x 3 ☺Multiply them ☺Double the result ☺Is it the same as the middle term?(disregard sign)

  12. ? P.S.T. Perfect Square Trinomial How to identify: ☺1st & last term must be perfect squares x2 + 6x + 9 THIS ☺Square root of the first ☺Square root of the last x 3x 3 IS ☺Multiply them A PST ☺Double the result ☺Is it the same as the middle term?(disregard sign)

  13. D.O.T.S. FLASH CARDS Is it PST? x2 – 10x + 25 U BETCHA

  14. D.O.T.S. FLASH CARDS Is it PST? x2 – 10x – 25 NO WAY DO YOU KNOW WHY?

  15. D.O.T.S. FLASH CARDS Is it PST? x2 + 20x + 40 NO WAY DO YOU KNOW WHY?

  16. D.O.T.S. FLASH CARDS Is it PST? 9m2 + 42m + 49 U BETCHA

  17. D.O.T.S. FLASH CARDS Is it PST? x2 + 16xy + 64y2 U BETCHA

  18. D.O.T.S. FLASH CARDS What would make this a PST? ±12x x2 _____ + 36

  19. D.O.T.S. FLASH CARDS What would make this a PST? ±36xy 4x2 _______ + 81y2

  20. D.O.T.S. FLASH CARDS What would make this a PST? + 9 x2 – 6x ____

  21. P.S.T. Perfect Square Trinomial How to factor x2 + 6x + 9 Square root of the first (x + 3) Sign of the second term 2 Square root of the last Quantity squared

  22. P.S.T. Perfect Square Trinomial How to factor 4m2 – 20m + 25 Square root of the first (2m – 5) Sign of the second term 2 Square root of the last Quantity squared

  23. FLASH CARDS Factoring Practice RECALL STEPS! 5x2 + 10xy 1. CMF BINOMIAL? 2. DOTS 5x(x + 2y) TRINOMIAL 3. PST GUESS

  24. FLASH CARDS Factoring Practice RECALL STEPS! x2 – 9y2 1. CMF BINOMIAL? 2. DOTS (x + 3y)(x – 3y) TRINOMIAL 3. PST GUESS

  25. FLASH CARDS Factoring Practice RECALL STEPS! 4x2 – 28x + 49 1. CMF BINOMIAL? 2. DOTS (2x – 7)2 TRINOMIAL 3. PST GUESS

  26. FLASH CARDS Factoring Practice RECALL STEPS! a2 – 2a – 15 1. CMF BINOMIAL? 2. DOTS (a – 5)(a + 3) TRINOMIAL 3. PST GUESS

  27. FLASH CARDS Solving Equations 2x3 + 8x2 – 42x = 0 Set equal to zero: Already is! 2x(x2 + 4x – 21) = 0 Factor left side: 2x(x + 7)(x – 3) = 0 More Factoring?? Factors = to 0: 2x= 0 or x + 7 = 0 or x – 3 = 0 Solve equations: x= 0 or x = -7 or x = 3

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