1. Warm-up
Solve each equation.
1. k2 = b2 = 169
3. m2 – 196 = c = 36
5. 6w2 – 24 = p2 = 4
k = ±9
b = ±13
m = ±14
c = 0
w = ±2

2. Factoring to Solve Quadratic Equations
Section 9.5
Factoring to Solve Quadratic Equations
Objective: I will solve quadratic equations by factoring.
Standards: 14.0, 23.0, 25.1

3. Zero Product Property:
If the product of two or more binomials equals 0, then each binomial equals 0.
(x + 3)(x + 2) = 0
(x + 3) = 0 and (x + 2) = 0

4. Solve each equation.
(x + 4)(x – 8) = 0
(x + 4) = 0
(x – 8) = 0
x + 4 = 0
x – 8 = 0 -4 +8
x = -4
x = 8

5. Solve each equation.
(5x + 4)(2x – 5) = 0
(5x + 4) = 0
(2x – 5) = 0
5x + 4 = 0
2x – 5 = 0
+5 +5
5x = -4
2x = 5

6. Solve each equation.
y(y – 1) = 0
y = 0
(y – 1) = 0
y – 1 = 0 +1
y = 1

7. Solving a quadratic:
If there are three terms:
Factor using the X or the box method.
Use the zero product property to solve each binomial.
Check your answer.

8. 12 3 4 7 Solve by factoring: x2 + 7x + 12 = 0 Factors of 12: 1 and 12

9. -28 4 -7 -3 Solve by factoring: b2 – 3b – 28 = 0 Factors of -28:
1 and -28 4 -7
2 and -14 -3
4 and -7
(b + 4)(b – 7)
= 0
b + 4 = 0
b – 7 = 0
b = -4
b = 7

10. Solve by factoring:
3a2 + 4a – 4 = 0
Multiply 3 & -4 3a
3a2 6a
-12 -2
-2a -4
-1 and 12 11
-2 and 6 4 a 2
-3 and 4 1
(3a – 2)(a + 2) = 0
3a – 2 = 0
a + 2 = 0
3a = 2
a = -2

11. Solve by factoring:
3x2 + 16x + 5 = 0
Multiply 3 & 5 x
3x2 1x 15 5
15x 5
1 and 15 16
3 and 5 8 3x 1
(3x + 1)(x + 5) = 0
3x + 1 = 0
x + 5 = 0
3x = -1
x = -5