1. Essential Question: Explain the process of solving a quadratic equation by factoring.

2. 10-4: Factoring Quadratic Equations Zero-Product Property For every real number a and b, if ab = 0, then a = 0 or b = 0 If (x + 3)(x + 2) = 0, then x + 3 = 0 or x + 2 = 0

3. 10-4: Factoring Quadratic Equations Example 1: Using the Zero-Product Property Solve (x + 5)(2x – 6) = 0 x + 5 = 0 - 5 - 5 x = -5 2x – 6 = 0 +6 +6 2x = 6 ÷2 ÷2 x = 3

4. 10-4: Factoring Quadratic Equations Y OUR T URN Solve each equation (x + 7)(x – 4) = 0 x = -7 or x = 4 (3y – 5)(y – 2) = 0 y = 5 / 3 or y = 2 (6k + 9)(4k – 11) = 0 k = - 3 / 2 or 11 / 4

5. How does this relate to factoring? (x + 3)(x + 2) = 0 is simply factored form To solve for a quadratic: Take a quadratic equation Set it equal to 0 Factor it Set each ( ) equal to 0 and solve for x

6. 10-4: Factoring Quadratic Equations Reminders of how to factor Get one side of the equation = 0 Look for two numbers that Multiply to get the product of the first & last numbers Add to get the middle number Write your parenthesis repeating the first term (without the square) and using each of the two numbers above Take out any GCFs

7. 10-4: Factoring Quadratic Equations Example 2: Solve by factoring Solve x 2 + 6x + 8 = 0One side is = 0 x 2 + 6x + 8 = 0Multiply = 8, add = 6 (x + 4)(x + 2) = 0 x + 4 = 0orx + 2 = 0Set each ( ) = 0 x = -4orx = -2 Y OUR T URN Solve x 2 – 8x – 48 = 0 x = 12 or x = -4

8. Example 2: Solve by factoring Solve 2x 2 – 5x = 88Subtract 88 from both sides 2x 2 – 5x – 88 = 0One side is = 0 (2x – 16)(2x + 11)Multiply: -176, add: -5 (-16 & 11) 2(x – 8)(2x + 11)Take out GCF and remove it x – 8 = 0or2x + 11 = 0 x = 8or2x = -11 x = - 11 / 2

9. 10-4: Factoring Quadratic Equations Y OUR T URN : S OLVE THE F OLLOWING x 2 – 12x = -36 x = 6 3x 2 – 2x = 21 x = - 7 / 3 or x = 3

10. Assignment Worksheet #10-4 1 – 29, odds