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5.4 Factoring Quadratic Expressions

5.4 Factoring Quadratic Expressions. 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. By Graphing. y = (x + 2)(x – 4).

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5.4 Factoring Quadratic Expressions

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  1. 5.4 Factoring Quadratic Expressions

  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. 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. Golden Rules of Factoring

  5. Example: Factor out the greatest common factor • 4x2 + 20x -12

  6. Practice: Factor each expression a) 9x2 + 3x – 18 b) 7p2 + 21 c) 4w2 + 2w • Solutions: • a.) 3(3x2 + x – 6) • b) 7(p2 + 3) • c) 2w(2w + 1)

  7. Factor Diamonds x² + 8x + 7 =0 7 7 1 8 = (x + 1) (x + 7) = 0 So your answers are -1 and -7

  8. Practice: Solve by a factor diamond • X2 + 15x + 36 (x+3)(x+12)

  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 2 Multiply by 2 to get rid of the fraction = (x + 6) (2x + 1) =0 So your answers are -6 and -1/2

  10. Practice: Solve using Bottom’s Up/Barrowing Method • 2x2 – 19x + 24 (x-8)(2x-3)

  11. Factor by Grouping 2x² – 7x – 15 =0 2x² – 10x + 3x – 15 =0 -30 -10 3 Note: you are on the right track because you have (x-5) in both parenthesis -7 2x(x – 5) + 3(x – 5) =0 (2x + 3)(x – 5)=0 So your answers are -3/2 and 5

  12. Practice: Factor by Grouping 3x2 + 7x - 20 (x+4)(3x-5)

  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. Practice Problems: Solve using any method • 3x2 – 16x – 12 • 4x2 + 5x – 6 • 4x2 – 49 • 2x2 + 11X + 12 • Solutions: • a) (x-6)(3x+2) • (x+2)(4x-3) • (2x+7)(2x-7) • (x+4)(2x+3)

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