Luttrell 2012
118
Name: ______________________
Date: _____
8e – Solve by Factoring
Once you know how to factor, then you are able to solve many quadratic equations for the
variable. Most equations will follow the steps as in the e
x
ample below.
E
x
ample: 2
x
2
=
x
2
+ 5
x
- 6
2
x
2
-
x
2
- 5
x
+ 6 = 0
Bring terms to one side of the equation.
x
2
- 5
x
+ 6 = 0
Simplif
y
(
x
- 2)(
x
- 3) = 0 Factor
x
- 2 = 0 Or
x
- 3 = 0
If
ab
= 0, then either
a
= 0 or
b
= 0.
x
∈
{2, 3}
Solve each equation for the variable.
E
x
ample: 0 = 2
x
2
+ 6
x
- 20
Fill in the blanks!
0 = 2(
x
2
+ 3
x
-
±
)
0 = 2(
x
+
±
)(
x
-
±
)
x
+
±
= 0 Or
x
- 2 = 0
x
∈
{2, -5}
Solve b
y
factoring:
1.
x
2
- 7
x
+ 6 = 0
2.
x
2
- 3
x
+ 2 = 0
3.
x
2
- 7
x
+ 12 = 0
4.
x
2
- 3
x
= 4
5.
x
2
+ 5
x
= - 4
6.
x
2
+ 13
x
+ 12 = 0
7.
x
2
+ 5
x
= 14
8.
x
2
- 8
x
+ 12 = 0
9.
x
2
+ 9
x
= -14
10. 2
x
2
+
x
= 6
11. 4
x
2
+ 9
x
= -5
12. 12
x
2
-
x
= 20
