Download Math 0312 Review for the Final Exam

Math 0312 Review for the Final Exam
PROBLEMS
1. Factor: 27x3 – 1
2. Solve: | 2x – 5 | + 7 = 14
3. Find the equation of a line through the
points (3, –2) and (1, –4).
4. Let f(x) = 5x2 – 6x – 7. Find f(–2).
3
5. find the domain of
.
2x  6
x 2  5x  4
6. Reduce: 2
x  8x  9
7. Find the equation of the line parallel to
6x – 3y = 15 and through the point (2, –1).
4x
2
 2
8. 2
x  1 5x  5x
3
2

9.
x 1 x  3
2
3

10. Simplify: x x  6
4
5

x6 x
1 x
5
x


11. Solve:
x  2 x  2 x 1
20  45  75
12. Simplify:
1
13. Simplify: x 4 ( xy) 4
ANSWERS
1. (3x – 1) (9x2 + 3x + 1)
2. 6, –1
3. y = x – 5
4. 25
5. (–∞, 3) U (3, ∞)
x4
x9
7. y = 2x – 5
6.
10 x 2
8.
x 1
x  11
9.
( x  1) ( x  3)
5x  6
10.
 x  30
4
5
12.  5  5 3
1
13. 15
11.
x 4 y4
14. Rationalize the denominator:
6
2 3
15. Solve: x  1  2  3
3  2i
16. Divide:
1 i
17. Solve by completing the square:
2x2 – 2x - 1 = 0
18. Solve: –x2 = 1 – 5x
2
1
19. Solve: x 3  x 3  12  0
x 1
0
20. Solve:
2x  1
14. 2 6  3 2
15. 24
1 5
 i
2 2
1
3
17. 
2 2
5  21
18.
2
19. 64, –27
16.
 1 
20.   ,1
 2 