Advanced Algebra
Mid-term Exam Review
Factoring
Factor each polynomial completely.
Common Factors:
1.
5x + 20
2.
3x2 – 6x
3.
24x3 + 40x2
4.
10x + 30
5.
2x2 – 6x
6.
24x3 + 40x2 + 4x
Difference of Squares:
7.
x2 – 9
8.
4m2 – 25
10.
18m2 – 32
12.
x2 – 10x + 16
9.
3x2 – 75
Trinomials:
11.
x2 + 7x + 12
13.
a2 – 7a – 30
14.
x2 + 11x + 28
15.
x2 – 14x + 45
16.
a2 – 5a – 14
17.
2x2 + 11x + 5
18.
7m2 – 10m + 3
19.
3x2 – 8x – 16
20.
2x2 + 7x + 3
21.
7m2 + 4m  3
22.
2x2 + 21x – 11
Sum & Difference of Cubes:
23.
x3 + 125
24
x3 – 64
26.
8x3 + 1
28.
x3 + 4x2 + 6x + 24
30.
3x3 – 6x2 – 4x + 8
25.
2x3 – 16
Grouping:
27.
x3 + 2x2 – 5x – 10
29.
2x3 – 8x2 + x – 4
Answers:
1. 5(x + 4)
2. 3x(x – 2)
3. 8x2(3x + 5)
4. 10(x + 3)
5. 2x(x – 3)
2
6. 4x(6x + 10x + 1)
7. (x + 3)(x – 3)
8. (2m + 5)(2m – 5)
9. 3(x + 5)(x – 5)
10. 2(3m + 4)(3m – 4)
11. (x + 4)(x + 3)
12. (x – 8)(x – 2)
13. (a – 10)(a + 3)
14. (x + 7)(x + 4)
15. (x – 9)(x – 5)
16. (a – 7)(a + 2)
17. (2x + 1)(x + 5)
18. (7m – 3)(m – 1)
19. (3x + 4)(x – 4)
20. (2x + 1)(x + 3)
21. (7m – 3)(m + 1)
2
2
22. (2x – 1)(x + 11)
23. (x + 5)(x – 5x + 25)
24. (x – 4)(x + 4x + 16)
25. 2(x – 2)(x2 + 2x + 4)
26. (2x + 1)(4x2 – 2x + 1)
27. (x + 2)(x2 – 5)
2
2
28. (x + 4)(x + 6)
29. (x – 4)(2x + 1)
30. (x – 2)(3x2 – 4)