1. 9-5 Factoring to Solve Quadratic Equations
Hubarth
Algebra

2. For every real number a, b, if ab = 0, then a = 0 or b = 0.
Zero Product Property
For every real number a, b, if ab = 0, then a = 0 or b = 0.
EXAMPLE If (x + 3)(x + 2) = 0, then x + 3 = 0 and x + 2 = 0
Ex 1 Using the Zero Product Property
Solve (2x + 3)(x – 4) = 0 by using the Zero-Product Property.
2x + 3 = or x – 4 = 0
x = 4
2x = –3
x = – 3 2

3. Ex 2 Solving by Factoring
Solve x2 + x – 42 = 0 by factoring.
x2 + x – 42 = 0
(x + 7)(x – 6) = 0
x + 7 = 0 or x – 6 = 0
x = –7 or x = 6

4. Ex 3 Solving by Factoring
Solve 3x2 – 2x = 21 by factoring.
3x2 – 2x – 21 = 0
(3x + 7)(x – 3) = 0
3x + 7 = 0 or x – 3 = 0
3x = –7
x = 3
x = – 7 3

5. Practice
Find the zeroes of each equation.
a. 𝑥+7 𝑥−4 = 𝑏. 3𝑦−5 𝑦−2 = 𝑐. (6𝑘+9)(4𝑘−11)
x =−7, 4
𝑦= 5 3 , 2
𝑘=− 9 6 , 11 4
2. Solve 𝑥 2 −8𝑥−48=0 𝑏𝑦 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑛𝑔.
12, -4
3. Solve 2𝑥 2 −5𝑥=88
𝑥=−5.5, 8