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Warm Up Find each product. 1. ( x + 2)( x + 7) 2. ( x – 11)( x + 5) 3. ( x – 10) 2

Warm Up Find each product. 1. ( x + 2)( x + 7) 2. ( x – 11)( x + 5) 3. ( x – 10) 2 Factor each polynomial. 4 . x 2 + 12 x + 35 5. x 2 + 2 x – 63 6. x 2 – 10 x + 16 7. 2 x 2 – 16 x + 32. x 2 + 9 x + 14. x 2 – 6 x – 55. x 2 – 20 x + 100.

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Warm Up Find each product. 1. ( x + 2)( x + 7) 2. ( x – 11)( x + 5) 3. ( x – 10) 2

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  1. Warm Up • Find each product. • 1. (x + 2)(x + 7) 2. (x – 11)(x + 5) • 3. (x – 10)2 • Factor each polynomial. • 4. x2 + 12x + 35 5. x2 + 2x – 63 • 6. x2 – 10x + 16 7. 2x2 – 16x + 32 x2 + 9x + 14 x2 – 6x – 55 x2 – 20x + 100 (x + 5)(x + 7) (x– 7)(x + 9) (x – 2)(x – 8) 2(x – 4)2

  2. Learning Target Students will be able to: Solve quadratic equations by factoring.

  3. You have solved quadratic equations by graphing. Another method used to solve quadratic equations is to factor and use the Zero Product Property.

  4. Use the Zero Product Property to solve the equation. (x – 7)(x + 2) = 0 x – 7 = 0 or x + 2 = 0 x = 7 or x = –2 (x + 4)(x – 3) = 0 The solutions are 7 and –2. x + 4 = 0 or x – 3 = 0 • x = –4 or x = 3 (x – 2)(x) = 0 The solutions are –4 and 3. x= 0 or x – 2 = 0 x = 2 The solutions are 0 and 2.

  5. Helpful Hint To review factoring techniques, see lessons 8-3 through 8-5. If a quadratic equation is written in standard form, ax2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property.

  6. x = 4 or x = 2 The solutions are 4 and 2. Solve the quadratic equation by factoring. x2 – 6x + 8 = 0 (x – 4)(x – 2) = 0 x – 4 = 0 or x – 2 = 0

  7. x2 + 4x = 21 –21 –21 x2 + 4x – 21 = 0 x = –7 or x =3 The solutions are –7 and 3. x2 + 4x = 21 (x + 7)(x –3) = 0 x + 7 = 0 or x – 3 = 0

  8. –2x2 = 20x + 50 +2x2 +2x2 0 = 2x2 + 20x + 50 Solve the quadratic equation by factoring. –2x2 = 20x + 50 0 = 2(x2 + 10x + 25) 0 = 2(x + 5)(x + 5) x + 5 = 0 x = –5

  9. Helpful Hint (x – 3)(x – 3) is a perfect square. Since both factors are the same, you solve only one of them.

  10. Solve the quadratic equation by factoring. Check your answer. x2 – 6x + 9 = 0 (x – 3)(x – 3) = 0 x – 3 = 0 x = 3

  11. x2 + 4x = 5 –5 –5 x2 + 4x – 5 = 0 Solve the quadratic equation by factoring. x2 + 4x = 5 (x – 1)(x + 5) = 0 x – 1 = 0 or x + 5 = 0 x = 1 or x = –5 The solutions are 1 and –5.

  12. Solve the quadratic equation by factoring. 30x = –9x2 – 25 9x2 + 30x + 25 = 0 (3x + 5)(3x + 5) = 0 3x + 5 = 0

  13. The height in feet of a diverabove the water can be modeled by h(t) = –16t2 + 8t + 8, where t is time in seconds after the diver jumps off a platform. Find the time it takes for the diver to reach the water. h = –16t2 + 8t + 8 2t + 1 = 0 or t – 1= 0 0 = –16t2 + 8t + 8 2t = –1 or t = 1 0 = –8(2t2 – t – 1) It takes the diver 1 second to reach the water.

  14. HW pp. 633-635/20-44,46-50,56-67

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