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)