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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Factoring Quadratic Expressions
Factor each completely.
1)
x
2
− 7
x − 18 2)
p
2
− 5
p − 14
3)
m
2
− 9
m + 8 4)
x
2
− 16
x + 63
5)
7
x
2
− 31
x − 20 6)
7
k
2
+ 9
k
7)
7
x
2
− 45
x − 28 8)
2
b
2
+ 17
b + 21
9)
5
p
2
−
p − 18 10)
28
n
4
+ 16
n
3
− 80
n
2
-1-
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Worksheet by Kuta Software LLC
11)
3
b
3
− 5
b
2
+ 2
b 12)
7
x
2
− 32
x − 60
13)
30
n
2
b − 87
nb + 30
b 14)
9
r
2
− 5
r − 10
15)
9
p
2
r + 73
pr + 70
r 16)
9
x
2
+ 7
x − 56
17)
4
x
3
+ 43
x
2
+ 30
x 18)
10
m
2
+ 89
m − 9
Critical thinking questions:
19) For what values of
b is the expression
factorable?
x
2
+
bx + 12
20) Name four values of
b which make the
expression factorable:
x
2
− 3
x +
b
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Factoring Quadratic Expressions
Factor each completely.
1)
x
2
− 7
x − 18
(
x − 9
)(
x + 2
)
2)
p
2
− 5
p − 14
(
p + 2
)(
p − 7
)
3)
m
2
− 9
m + 8
(
m − 1
)(
m − 8
)
4)
x
2
− 16
x + 63
(
x − 9
)(
x − 7
)
5)
7
x
2
− 31
x − 20
(
7
x + 4
)(
x − 5
)
6)
7
k
2
+ 9
k
k
(
7
k + 9
)
7)
7
x
2
− 45
x − 28
(
7
x + 4
)(
x − 7
)
8)
2
b
2
+ 17
b + 21
(
2
b + 3
)(
b + 7
)
9)
5
p
2
−
p − 18
(
5
p + 9
)(
p − 2
)
10)
28
n
4
+ 16
n
3
− 80
n
2
4
n
2
(
7
n − 10
)(
n + 2
)
-1-
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Worksheet by Kuta Software LLC
11)
3
b
3
− 5
b
2
+ 2
b
b
(
3
b − 2
)(
b − 1
)
12)
7
x
2
− 32
x − 60
(
7
x + 10
)(
x − 6
)
13)
30
n
2
b − 87
nb + 30
b
3
b
(
2
n − 5
)(
5
n − 2
)
14)
9
r
2
− 5
r − 10
Not factorable
15)
9
p
2
r + 73
pr + 70
r
r
(
p + 7
)(
9
p + 10
)
16)
9
x
2
+ 7
x − 56
Not factorable
17)
4
x
3
+ 43
x
2
+ 30
x
x
(
x + 10
)(
4
x + 3
)
18)
10
m
2
+ 89
m − 9
(
m + 9
)(
10
m − 1
)
Critical thinking questions:
19) For what values of
b is the expression
factorable?
x
2
+
bx + 12
13, 8, 7, −13, −8, −7
20) Name four values of
b which make the
expression factorable:
x
2
− 3
x +
b
Many answers. Ex: 0, 2, −4, −10, −18
-2-
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