1. What you will learn A review of all kinds of factoring (yippee)
How to solve a quadratic by factoring
The zero product property

2. Solving Quadratic Equations by Factoring
Vocabulary:
Monomial: An expression that has only one term. e.g. 2x
Binomial: An expression with two terms e.g.:
x + 5
Trinomial: An expression with three terms e.g.:
x2 + 2x + 3
Factoring: Writing a trinomial as a product of binomials (un “foiling”).
Objective: 5.2 Solving Quadratic Equations by Factoring

3. Examples
Factor x2 – 12x – 28
This puts the quadratic equation in intercept form.
Objective: 5.2 Solving Quadratic Equations by Factoring

4. You Try
Factor x2 – 2x - 48
Objective: 5.2 Solving Quadratic Equations by Factoring

5. When “A” is not 1 Factor 3x2 – 17x + 10
Objective: 5.2 Solving Quadratic Equations by Factoring

6. You Try
Factor 4y2 – 4y - 3
Objective: 5.2 Solving Quadratic Equations by Factoring

7. Special Factoring Patterns
Pattern name Pattern Example
Diff of Squares a2 – b2 = (a + b)(a – b) x2 – 9
(x + 3)(x – 3)
Perfect Sq.
Trinomial a2 + 2ab + b2 x2 + 12x + 36
(a + b)2 (x + 6)2
a2 – 2ab + b2 x2 – 8x + 16
(a – b)2 (x – 4)2
Objective: 5.2 Solving Quadratic Equations by Factoring

8. Factoring with Special Patterns - Examples
Difference of squares: 4x2 – 25
Perfect square trinomial: 9y2 + 24y + 16
Perfect square trinomial: 49r2 – 14r + 1
Objective: 5.2 Solving Quadratic Equations by Factoring

9. You Try Factor the following: 1. x2 – 25 2. 4x2 + 12x + 9
Objective: 5.2 Solving Quadratic Equations by Factoring

10. Factoring Monomials First
Factor the following:
1. 5x2 – 20
2. 6p2 + 15p + 9
3. 2u2 + 8u
Objective: 5.2 Solving Quadratic Equations by Factoring

11. You Try Factor the following: 1. 14x2 + 2x – 12 2. 3v2 – 18v
Objective: 5.2 Solving Quadratic Equations by Factoring

12. Finally…we are going to solve these things
Zero Product Property:
Let A and B be real numbers or algebraic expressions. If
AB = 0 then A = 0 or B = 0.
Examples:
(x – 3)(x + 4) = 0 then either x – 3 equals zero of x + 4 equals zero.
Objective: 5.2 Solving Quadratic Equations by Factoring

13. Solving Quadratic Equations
Solve:
1. x2 + 3x – 18 = 0
2. 2t2 – 17t + 45 = 3t - 5
Objective: 5.2 Solving Quadratic Equations by Factoring

14. You Try Solve. 1. 9t2 – 12t + 4 = 0 2. 3x – 6 = x2 - 10
Objective: 5.2 Solving Quadratic Equations by Factoring

15. A Word Problem
You have made a rectangular stained glass window that is 2 feet by 4 feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of the border be?
Area of border = area of border and wind. – area of wind.
Objective: 5.2 Solving Quadratic Equations by Factoring

16. Finding “Zeros” of Quadratic Functions
Two Ways:
1. Factoring! y = x2 – x – 6
2. Calculator!
Objective: 5.2 Solving Quadratic Equations by Factoring

17. Homework
page 260, even, 36, 38, 47, even, even, even
Objective: 5.2 Solving Quadratic Equations by Factoring