FACTORING PROBLEMS
Courtesy of Harold Hiken
Factor each of the following expressions either by inspection or by using the grouping method discussed in your text. If a greatest common factor can be removed first, factor it out. If the problem cannot be factored, state so.
1)
2x2
+ 7x + 3 8)
6x2 + x – 1 15) 4t2 – 5t – 6
2)
3y2
+ 13y + 4 9)
8m2 – 10m – 3 16) 8k2 + 2k – 15
3)
3a2
+ 10a + 7 10)
2a2 – 17a + 30 17) 8x2 – 14x + 3
4)
7r2
+ 8r + 1 11)
5a2 – 6 – 7a 18) 15p2 – p – 6
5)
4r2
+ r – 3 12)
11s + 12s2 – 5 19) 6q2 + 23q + 21
6)
3p2
+ 2p – 8 13)
3r2 + r – 10 20) 6x2 – x – 12
7)
15m2
+ m – 2 14)
4y2 + 69y + 17 21) 2 + 7b + 6b2
Answers:
1)
(2x
+ 1)(x + 3)
2)
(3y
+ 1)(y + 4)
3)
(3a
+ 7)(a + 1)
4)
(7r
+ 1)(r + 1)
5)
(4r
– 3)(r + 1)
6)
(3p
– 4)(p + 2)
7)
(5m
+ 2)(3m – 1)
8)
(3x
– 1)(2x + 1)
9)
(4m
+ 1)(2m – 3)
10)
(2a
– 5)(a – 6)
11)
(5a
+ 3)(a – 2)
12)
(4s
+ 5)(3s – 1)
13)
(3r
– 5)(r + 2)
14)
(4y
+ 1)(y + 17)
15)
(4t
+ 3)(t – 2)
16)
(4k
– 5)(2k + 3)
17)
(4x
– 1)(2x – 3)
18)
(5p
+ 3)(3p – 2)
19)
(3q
+ 7)(2q + 3)
20)
(3x
+ 4)(2x – 3)
21)
(3b
+ 2)(2b + 1)