Factor.

1) x² + 8x + 16

2) 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 eithera=0, b=0,

or both a and b equal 0.

Using the Zero Product Property, you know that either x + 3 = 0 or x – 5 = 0

Solve each equation.

x = - 3 or x = 5

Solutions: {-3, 5}

1. Solve (x + 3) (x – 5) = 0

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

3. Solve (3t + 5) (t – 3) = 0

Solve (y – 3) (2y + 6) = 0

a. {-3, 3}

b. {-3, 6}

c. {3, 6}

d. {3, -6}

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

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.

4. x2 + 4x + 3 = 0

5. x2 + 2x = 15

6. a2 = -6a + 27

Solve. a2 + 40 = 3a

1. {-8, 5}

2. {-5, 8}

3. {-8, -5}

4. {5, 8}

7. x2 – 9 = 0

8. x2 = 36

9. 9r2 = 16

10. x2 – 11x = 0

11. x2 = 4x

Homework

Homework 2/8 Worksheet

Review Sheet