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Warm-up

Warm-up. Factor. 1. p 2 + 6p – 27 2. p 2 – 15p – 16 3. k 2 + 9k + 20 4. k 2 – 14k + 24 . Warm-up. Factor. 1. p 2 + 6p – 27 2. p 2 – 15p – 16. -27. -16. -3. 9. 1. -16. 6. -15. ( p – 3)(p + 9). ( p + 1)(p – 16). Warm-up. Factor.

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Warm-up

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  1. Warm-up Factor. 1. p2 + 6p – 27 2. p2 – 15p – 16 3. k2 + 9k + 20 4. k2 – 14k + 24

  2. Warm-up Factor. 1. p2 + 6p – 27 2. p2 – 15p – 16 -27 -16 -3 9 1 -16 6 -15 (p – 3)(p + 9) (p + 1)(p – 16)

  3. Warm-up Factor. 3. k2 + 9k + 20 4. k2 – 14k + 24 20 24 4 5 -2 -12 9 -14 (k + 4)(k + 5) (k – 2)(k – 12)

  4. Section 10.4 Solving Radical Equations (Part 2) Standards: 2.0, 25.2 Objective: I will solve equations containing radicals.

  5. Extraneous Solutions: An answer that does not solve the original equation. x = 2 x2 = 4 (x)2 = 22 x = 2 x = -2

  6. Steps: Get the radicand by itself. Square both sides. Solve the remaining equation. Check your answer and identify extraneous solutions.

  7. Example 1: -6 2 -3 -1 (x + 2)(x – 3) = 0 x + 6 x2 = x + 2 = 0 x – 3 = 0 -x – 6 -x – 6 x2 – x – 6 = 0 x = -2 x = 3

  8. Example 1: check x = -2 & 3 ✔ -2 = 2 3 = 3 extraneous

  9. Example 2: 4 -1 -4 -5 (x – 1)(x – 4) = 0 5x – 4 x2 = x – 1 = 0 x – 4 = 0 -5x +4 -5x + 4 x2 – 5x + 4 = 0 x = 1 x = 4

  10. Example 2: check x = 1 & 4 ✔ ✔ 1 = 1 4 = 4

  11. Example 3: -20 -4 5 1 (x – 4)(x + 5) = 0 20 – x x2 = x – 4 = 0 x + 5 = 0 -20 + x -20 + x x2 + x – 20 = 0 x = 4 x = -5

  12. Example 3: check x = 4 & -5 ✔ 4 = 4 -5 = 5 extraneous

  13. Example 4: -56 -7 8 1 (x – 7)(x + 8) = 0 56 – x x2 = x – 7 = 0 x + 8 = 0 -56 + x -56 + x x2 + x – 56 = 0 x = 7 x = -8

  14. Example 4: check x = 7 & -8 ✔ 7 = 7 -8 = 8 extraneous

  15. Example 5: -12 3 -4 -1 (x + 3)(x – 4) = 0 x + 12 x2 = x + 3 = 0 x – 4 = 0 -x – 12 -x – 12 x2 – x – 12 = 0 x = -3 x = 4

  16. Example 5: check x = -3 & 4 ✔ -3 = 3 4 = 4 extraneous

  17. Example 6: -15 3 -5 -2 (x + 3)(x – 5) = 0 2x + 15 x2 = x + 3 = 0 x – 5 = 0 -2x – 15 -2x – 15 x2 – 2x – 15 = 0 x = -3 x = 5

  18. Example 6: check x = -3 & 5 ✔ -3 = 3 5 = 5 extraneous

  19. Example 7: 8 2 4 6 (x + 2)(x + 4) = 0 -8 – 6x x2 = x + 2 = 0 x + 4 = 0 8 + 6x 8 + 6x x2 + 6x + 8 = 0 x = -2 x = -4

  20. Example 7: check x = -2 & -4 -2 = 2 -4 = 4 extraneous extraneous no solution

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