Math 1010 Section 5 Review 2
Name:
Read all directions carefully. The review will be graded on completion and will be
worth 20 homework points. You can nd the complete solutions to the review posted
on my website www.math.utah.edu/~malone.
1. Using the rules of exponents simplify the following expression
(5z2 y 3x4 ) 2
(3y3z 4 x2 )10
Multiply out and then simplify the following expression (x 2)(3x +4)(7x2 5).
Factor completely 4x9 4x6 100x7 + 100x4 .
Find all solutions to x2 + 8x 20 = 16 + 3x
Find all solutions to 5x2 30x 41 = 14 + 9x 5x2
Find the domain of the function
p
p
301 3
46
2+x
x
5x 1
4
x
6
+
H (x) =
2
x 3x + 2
.
7. Perform the division
4x4 3x2 + 5
x2 2x + 1
.
8. Perform the division
3x5 + 20x4 + 13x3 + 2x2 25x 6
x+6
2.
3.
4.
5.
6.
22
9. Find all solutions to x2 44x 5 6x2 28
x 10 = 0
10. Simplify the following and be sure to write all exponents as positive powers
px y z
px y z
3
6
5 4
1
4 5 7
.
p
p
11. p
Multiply out and then simplify the following expression (x 2)(x + 6)(x
3).
p
p
4x = 0. (Be sure to check your
12. Find all solutions to the equation 2x 1
solutions)
p
pp
13. Find all solutions to the equation x + 1 = 3 3x + 1. (Do not check your
solutions).
p
p
14. Find all solutions to the equation x + 1 2x + 1 = 1 (Need to use quadradic
formula at the end).
15. Find all real and complex solutions of x4 1 = 0. (You can use the di erence
of two squares with 1 = i2 ).
16. Use completing the square to nd all the solutions to x2 + 8x 4 = 0
17. Use completing the square to nd all solutions to 2x2 14x 6 = 0
18. Use the quadradic formula to nd all complex and real solutions to 4x2 12x +
10 = 0
19. Find all real and complex solutions to 2x9 +3x8 +2x7 +3x6 2x3 3x2 2x 3 = 0
(Hint: Use grouping and 2 4 = 8).
20. Find all real solutions only to x8 + 3x7 x5 2x4 + 3x3 x 3 = 0 (Hint: x + 3
is a factor).