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Test #5a – Fall 1997
Beginning Algebra
Instructions: Please show all relevant work on your paper. This does not mean all of your tries at factoring, but it does mean the factors of the terms. You may use a calculator and a one-sided 8.5 x 11 sheet of notes. Please turn in your notes with your test. Good luck!
1. Find the GCF of
105a3b7c, 126a7b3c2, and 96a5b4d
2. Factor
3x2 ( 5x + 2
3. Factor
15x4y5 ( 21x3y3 ( 9xy2z3
4. Factor
5y(2x ( 5y) ( 2x(2x ( 5y)
5. Factor by grouping
12ax + 3ay ( 20bx ( 5by
6. Factor. Don't forget to remove any GCF first.
2x2 ( 10x + 12
7. Factor.
x2 + 3x ( 18
8. Factor
x2 ( 5x ( 24
9. Factor
4x2 + 16y2 .
10. Factor. Don't forget any GCF
12x2 ( 26xy + 10y2
11. Factor the perfect square trinomial completely.
4x2 ( 32x + 64
12. Factor the difference of the two perfect squares completely.
9x4 ( 9
13. Factor
9x2 ( 30xy + 25y2
14. Factor the difference of the two perfect squares completely.
18x2 ( 98y2
15. Factor the difference of the two perfect cubes completely.
27x3 ( 8x3y3
16. Factor the sum of the perfect cubes.
27x3 + 1
17. Solve for x.
7x(3x ( 8) = 0
18. Solve for x.
2x2 + 15 = 13x
19. Solve for x.
16x2 + 8x = 15
20. Solve for x.
27x3 ( 12x = 0
21. Solve for x by factoring by grouping.
x3 ( 4x = x2 ( 4
22. The length of a rectangle is 3cm greater than its width. The area of this
rectangle is 54 square cm. Find its length.
23. The sum of a positive number and twice its square is 21. Find the
number.
24. Expand.
(x ( 1)(x ( 2)(x + 2)
25. Simplify.
4 ( (5 ( 3)2 + 23
2 + | -4 |
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