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Factoring quadratic expressions

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GCF and Bottoms Up Method of factoring

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Factoring quadratic expressions

  1. 1. Factoring Quadratic Expressions
  2. 2. WAYS TO SOLVE A QUADRATIC EQUATION ax² + bx + c = 0• There are many ways to solve a quadratic.• The main ones are: – Graphing – Factoring – Bottom’s Up – Grouping – Quadratic formula – Completing the square
  3. 3. By Graphing y = (x + 2)(x – 4)By looking at the roots, we can get the solutions.Here, the solutions are -2 and 4.
  4. 4. Golden Rules of Factoring
  5. 5. Example: Factor out the greatest common factor• 4x2 + 20x -12
  6. 6. Practice: Factor each expressiona) 9x2 + 3x – 18 Solutions: a.) 3(3x2 + x – 6)b) 7p2 + 21 b) 7(p2 + 3)c) 4w2 + 2w c) 2w(2w + 1)
  7. 7. Factor Diamonds x² + 8x + 7 =0 7 7 1 8 = (x + 1) (x + 7) = 0 So your answers are -1 and -7
  8. 8. Practice: Solve by a factor diamond• X2 + 15x + 36 (x+3)(x+12)
  9. 9. Bottom’s up (Borrowing Method) 2x² + 13x + 6 =0 x² + 13x + 12 =0 12 12 1 = (x + 12) (x + 1) =0 13 2 2 = (x + 6) (x + 1) =0 Multiply by 2 to 2 get rid of the fraction = (x + 6) (2x + 1) =0 So your answers are -6 and -1/2
  10. 10. Practice: Solve using Bottom’s Up/Barrowing Method• 2x2 – 19x + 24 (x-8)(2x-3)
  11. 11. Factor by Grouping 2x² – 7x – 15 =0 -30 2x² – 10x + 3x – 15 =0-10 3 -7 Note: you are on the right 2x(x – 5) + 3(x – 5) =0 track because you have (x-5) in both (2x + 3)(x – 5)=0 parenthesis So your answers are -3/2 and 5
  12. 12. Practice: Factor by Grouping3x2 + 7x - 20 (x+4)(3x-5)
  13. 13. SHORTCUTS• a2 + 2ab + b2 (a+b)2 Example: 25x2 + 90x + 81 (5x + 9)2• a2 - 2ab + b2 (a - b)2 Example: 9x2 – 42x + 49 (3x – 7)2• a2 - b2 (a+b)(a - b) Example: x2 – 64 (x + 8)(x – 8)
  14. 14. Practice Problems: Solve using any method Solutions:• 3x2 – 16x – 12 a)(x-6)(3x+2)• 4x2 + 5x – 6• 4x2 – 49 c) (x+2)(4x-3)• 2x2 + 11X + 12 d)(2x+7)(2x-7) e)(x+4)(2x+3)
  • ElaineChristanto

    Aug. 27, 2019
  • sare01

    Nov. 19, 2015

GCF and Bottoms Up Method of factoring

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