Solving Quadratic Equations By Factoring Worksheet With Answers - Algebra 2, Glencoe Mcgraw-Hill
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1
2NAME
DATE
PERIOD
4-3
Study Guide and Intervention
Solving Quadratic Equations by Factoring
Factored Form
To write a quadratic equation with roots p and q, let (x - p)(x - q) = 0.
Then multiply using FOIL.
Example
Write a quadratic equation in standard form with the given roots.
7
1
a. 3, -5
b. -
−
,
−
8
3
(x - p)(x - q) = 0
(x - p)(x - q) = 0
Write the pattern.
(x - 3)[x - (-5)] = 0
(
) (
)
Replace p with 3, q with -5.
7
1
x -
-
−
x -
−
= 0
8
3
(x - 3)(x + 5) = 0
Simplify.
)
(
) (
7
1
2
x
+ 2x - 15 = 0
Use FOIL.
x +
−
x -
−
= 0
8
3
The equation x
2
+ 2x - 15 = 0 has roots
(8x + 7)
(3x - 1)
−
−
= 0
3 and -5.
8
3
24 (8x + 7)(3x - 1)
−−
= 24 0
24
24x
2
+ 13x - 7 = 0
The equation 24x
2
+ 13x - 7 = 0 has
7
1
roots -
−
and
−
.
8
3
Exercises
Write a quadratic equation in standard form with the given root(s).
1. 3, -4
2. -8, -2
3. 1, 9
x
2
+ x - 12 = 0
x
2
+ 10x + 16 = 0
x
2
- 10x + 9 = 0
4. -5
5. 10, 7
6. -2, 15
x
2
+ 10x + 25 = 0
x
2
- 17x + 70 = 0
x
2
- 13x - 30 = 0
1
2
3
7. -
−
, 5
8. 2,
−
9. -7,
−
3
3
4
3x
2
- 14x - 5 = 0
3x
2
- 8x + 4 = 0
4x
2
+ 25x - 21 = 0
2
4
1
10. 3,
−
11. -
−
, -1
12. 9,
−
5
9
6
2
2
2
5x
- 17x + 6 = 0
9x
+ 13x + 4 = 0
6x
- 55x + 9 = 0
5
3
2
2
1
1
13.
−
, -
−
14.
−
, -
−
15.
−
,
−
3
4
7
5
3
2
9x
2
- 4 = 0
8x
2
- 6x - 5 = 0
35x
2
- 22x + 3 = 0
7
7
1
3
1
1
16. -
−
,
−
17.
−
,
−
18.
−
,
−
8
2
2
4
8
6
2
2
2
16x
- 42x - 49 = 0
8x
- 10x + 3 = 0
48x
- 14x + 1 = 0
17
Chapter 4
Glencoe Algebra 2
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