HW #86-­‐KEY Name___________________________________
225-­‐Honors Algebra 2 Expressions
Date________________
Period____
Factoring Review Solutions Kuta Software - Infinite Algebra 2
Factoring Quadratic
Factor each completely.
1) x 2 − 7 x − 18
2) p 2 − 5 p − 14
( x − 9)( x + 2)
3) m 2 − 9m + 8
( p + 2)( p − 7)
4) x 2 − 16 x + 63
(m − 1)(m − 8)
5) 7 x 2 − 31 x − 20
( x − 9)( x − 7)
6) 7k 2 + 9k
(7 x + 4)( x − 5)
7) 7 x 2 − 45 x − 28
k(7k + 9)
8) 2b 2 + 17b + 21
(7 x + 4)( x − 7)
9) 5 p 2 − p − 18
(2b + 3)(b + 7)
10) 28n 4 + 16n 3 − 80n 2
(5 p + 9)( p − 2)
4n 2 (7n − 10)(n + 2)
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Worksheet by Kuta Softwar
HW #86-­‐KEY 225-­‐Honors Algebra 2 Factoring Review Solutions 11) 3b 3 − 5b 2 + 2b
12) 7 x 2 − 32 x − 60
b(3b − 2)(b − 1)
13) 30n 2 b − 87nb + 30b
(7 x + 10)( x − 6)
14) 9r 2 − 5r − 10
3b(2n − 5)(5n − 2)
15) 9 p 2 r + 73 pr + 70r
Not factorable
16) 9 x 2 + 7 x − 56
r( p + 7)(9 p + 10)
17) 4 x 3 + 43 x 2 + 30 x
Not factorable
18) 10m 2 + 89m − 9
x( x + 10)(4 x + 3)
(m + 9)(10m − 1)
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:
x2 − 3x + b
13, 8, 7, −13, −8, −7
Many answers. Ex: 0, 2, −4, −10, −18
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Worksheet by Kuta Software LLC
HW #86-­‐KEY Name___________________________________
225-­‐Honors Algebra 2 Kuta Software - Infinite Algebra 2
Factoring: All Techniques Combined (Hard)
Factoring Review Solutions Date________________ Period____
Factor each.
1) x 3 − 5 x 2 − x + 5
2) x 4 − 2 x 2 − 15
( x − 5)( x + 1)( x − 1)
3) x 6 − 26 x 3 − 27
(x 2 − 5)( x 2 + 3)
4) x 6 + 2 x 4 − 16 x 2 − 32
( x − 3)( x 2 + 3 x + 9)( x + 1)( x 2 − x + 1)
5) x 4 − 13 x 2 + 40
(x 2 + 2)( x 2 + 4)( x + 2)( x − 2)
6) x 9 − x 6 − x 3 + 1
( x 2 − 5)( x 2 − 8)
7) x 6 − 4 x 2
(x − 1) 2( x 2 + x + 1) 2( x + 1)( x 2 − x + 1)
8) x 4 + 14 x 2 + 45
x 2 ( x 2 − 2)( x 2 + 2)
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(x 2 + 5)( x 2 + 9)
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Worksheet by Kuta Software LLC
HW #86-­‐KEY 225-­‐Honors Algebra 2 Factoring Review Solutions 9) 2 x 4 + x 2 − 6
10) 2 x 2 − 13 x + 20
(2 x 2 − 3)( x 2 + 2)
11) 4 x 3 − x 2 − 4 x + 1
(2 x − 5)( x − 4)
12) 4 x 8 − 61 x 4 + 225
(4 x − 1)( x + 1)( x − 1)
13) 5 x 2 + 24 x − 5
(2 x 2 + 5)(2 x 2 − 5)( x 2 + 3)( x 2 − 3)
14) 5 x 2 + 29 x + 20
(5 x − 1)( x + 5)
15) 4 x 2 + 4 x − 15
(5 x + 4)( x + 5)
16) 10 x 3 − 8 x 2 + 25 x − 20
(2 x − 3)(2 x + 5)
17) −64 x 3 + 125 = 0
(5 x − 4)(2 x 2 + 5)
18) 8 x 4 + 10 x 2 − 3
(4 x − 5)(−16 x 2 − 20 x − 25) = 0
(2 x + 1)(2 x − 1)(2 x 2 + 3)
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Worksheet by Kuta Software LLC