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Factor. x ² + 8x + 16 y² – 4y – 21

Do Now. Factor. x ² + 8x + 16 y² – 4y – 21. Zero Product Property. If two numbers multiply to zero, then either one or both numbers has to equal zero. If a • b = 0 then either a=0, b=0, or both a and b equal 0. 1. Solve (x + 3) (x – 5) = 0.

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Factor. x ² + 8x + 16 y² – 4y – 21

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  1. Do Now Factor. x² + 8x + 16 y² – 4y – 21

  2. Zero Product Property If two numbers multiply to zero, then either one or both numbers has to equal zero. If a • b = 0 then either a=0, b=0, or both a and b equal 0.

  3. 1. Solve (x + 3) (x – 5) = 0 Using the Zero Product Property, you know that either x + 3 = 0or x – 5 = 0 Solve each equation. x = - 3 or x = 5 Solutions: {-3, 5}

  4. 2. Solve (2a + 4) (a + 7) = 0

  5. 3. Solve (3t + 5) (t – 3) = 0

  6. Solve (y – 3) (2y + 6) = 0 a. {-3, 3} b. {-3, 6} c. {3, 6} d. {3, -6}

  7. Quadratic Equations A quadratic equation is an equation that contains a variable squared in it, and no higher powers of the variable. Ex: x2 + 3x – 10 = 0 y2 – 16 = 0 6a + a2 = 16

  8. Solving Quadratic Equations The zero product property can be used to solve quadratic equations. Steps: 1) Set the equation equal to zero. * You want the squared term to be positive 2) Factor. 3) T out. 4) Check with your calculator.

  9. 4. x2 + 4x + 3 = 0

  10. 5. x2 + 2x = 15

  11. 6. a2 = -6a + 27

  12. Solve. a2 + 40 = 3a • {-8, 5} • {-5, 8} • {-8, -5} • {5, 8}

  13. 7. x2 – 9 = 0

  14. 8. x2 = 36

  15. 9. 9r2 = 16

  16. 10. x2 – 11x = 0

  17. 11. x2 = 4x

  18. Homework Homework 2/8 Worksheet Review Sheet

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