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Factoring Polynomials
Name ____________________________
Directions: Factor each expression completely and find the answer in the answer chart.
Use the corresponding letters to decode the message below. Be careful! There are
more answers than questions. Be sure to show all work!
___ ___ ___ ___ ___ ___ ___ ___ ___
1
3
12
5
7
8
14
10
___ ___ ___ ___ ___ ___ ___
11
2
2
17
___ ___
7
1
14
10
4
___ ___
___ ___ ___ ___
14
17
16
___ ___ ___ ___
6
9
___ ___ ___
5
6
2
3
12
14
13
___ ___ ___
13
3
17
___ ___ ___ ___ ___ ___ !
17
3
15
2
8
1. Factor: x 2 − 2 x − 15
2. Factor: 16 x 2 − 81
3. Factor: 24 x 3 y − 54 xy
4. Factor: 4 x 6 − 64 x 2
5. Factor: x8 − 1
6. Factor: x 4 y 2 − 4 x 3 y 2 − 12 x 2 y 2
7. Factor: x 2 a + 4 x a − 32
8. Factor: 12 x −3 − 3 x −5
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16
17
2
9. Factor: − x 2 − 9 x + 22
10. Factor x3 − 5 x 2 + 2 x − 10 by grouping
11. Factor: x8 − y 4
12. Factor: 8 x 2 − 10 x − 3
13. Factor: −3x 4 + 30 x3 − 75 x 2
14. Factor: 4 x( x + 1) − 7( x + 1) 2
15. Factor: 5 x 5 − 10 x 4 + 25 x 3 − 50 x 2
16. Factor: x 6 a − 4 x 4 a
17. Factor: x3 − 8
Find your answers in the chart
below:
A
D
G
J
M
P
S
V
6 xy (2 x − 3)(2 x + 3)
x y ( x + 6)( x − 2)
2
2
x y ( x − 6)( x + 2)
2
2
4 x ( x − 16)
2
4
( x + 1)( x − 1)( x − 5)
( x 2 − y )( x 2 + y )( x 4 + y 2 )
x 4 a ( x a − 2)( x a + 2)
−5
3x (4 x − 1)
2
B
E
H
K
N
Q
T
W
−( x + 11)( x − 2)
(4 x − 9)(4 x + 9)
4 x ( x + 4)( x − 2)( x + 2)
2
2
−3x ( x − 5)
2
2
( x 2 + 2)( x − 5)
( x 4 − y 2 )( x 4 + y 2 )
( x − 1)( x + 1)( x 2 + 1)( x 4 + 1)
6 xy (4 x − 9)
2
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C
F
I
L
O
R
U
Y
(4 x + 1)(2 x − 3)
( x − 5)( x + 3)
−( x + 1)(3x + 7)
( x − 2)( x 2 + 2 x + 4)
( x a + 8)( x a − 4)
3x −5 (2 x − 1)(2 x + 1)
(− x + 1)(3x + 7)
5 x 2 ( x 2 + 5)( x − 2)