1. Lesson 10.5
Factoring
Objective: To factor a quadratic trinomial of the form
Factoring a trinomial is the opposite of multiplying two binomials.
Example: Factor
You need to find two numbers whose sum is 5 and whose product is 6
(x + ? )(x + ? )
2 and 3
(x + 2)(x + 3)
Check by multiplying (x +2)(x + 3)=

2. EX: Factor
Find two numbers that
+ to get 7
 to get 12
(x + 3)(x + 4)
3 and 4
EX: Factor
Find two numbers that
+ to get 4
x to get -12
(x + 6) (x – 2)
6 and –2

3. Example: Factor
Find two numbers that
+ to get –5
 to get 6
–2 and –3
(x – 2)(x – 3)
Find two numbers that
+ to get –7
 to get –30
Example: Factor
(x – 10)(x + 3)
–10 and 3

4. Solving Quadratic Equations by Factoring
EX: Solve for x by factoring.
Find two #’s that + to get 8 and x to get 12
2 and 6
(x + 2)(x + 6) = 0
Use zero product property to solve for x.
x + 2 = 0 and x + 6 = 0
–2 –2
–6 –6
x = -2
x = -6

5. EX: Solve for x
Numbers that + to get 7, x to get –18
9 and –2
(x + 9)( x – 2) = 0
x + 9 = 0
x – 2 = 0
x = – 9 and 2