13. Multiply the following polynomials and simplify:
(8x + 1)(2x5 + 9x2 - 3)
16x6 + 2x5 + 72x3 + 9x2 - 24x - 3
(5x5 + 8x3 - 10)(1x5 + 6x3)
5x10 + 38x8 + 48x6 - 10x5 - 60x3
14. Divide:
12x3 + 36x2 - 6x - 18 / 3x + 9
4x2 - 2
15. Find the greatest common factor of the following terms:
100, 33, 15
1
18x9y3, 84x9y8, 81x6y7
3x6y3
16. Factor the following polynomials:
8x5 - 29x4 + 15x3
8x3(x - 3)(x -
5
8
)
x2 + 6x - 27
(x - 3)(x + 9)
x8 + 6x7 - 112x6
x6(x + 14)(x - 8)
17. For question 16, exercises b) and c), solve for x:
x =
3
and
-9
x =
0
,
-14
and
8
18. You have 8 CDs. How many different ways can you listen to them?
40320
19. Use the following data to construct a box and whiskers plot:
27, 39, 7, 33, 8, 12, 28, 20, 4, 23
20. A bag contains 2 blue balls, 5 red balls, and 7 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
50.00%
A blue ball or red ball?
50.00%
Two red balls?
12.76%
A blue ball and a white ball?
7.14%
21. Solve and graph the following systems of linear equations:
x + y = 17 x - y = -12
A(2.5,14.5)
3x - 4y = 7 10x + 7y = -19
B(-0.44,-2.08)
22. Write the following fractions in simplest form:
21x7y5
84x6y7
x
4y2
(x + 4)
(x2 + 8x + 16)
1
x + 4
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
-5x = x2 + 6
x1 = -2, x2 = -3
24. Convert the following repeating decimal into a fraction:
x =
0.510
505
990
25. Solve the following equation:
-
2x + 6
- 4 = -20
x = 125
26. Rationalize the denominator of each fraction below:
21
15 +
2
315 - 21
2
223
27. Use a trigonometric ratio to find x:
x = 29.44 cm
28. The sum of two consecutive odd integers is 40. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=19, b=21
29. After you leave your house, you walk 8 blocks south and 15 blocks east. How far are you from your house?
I am
17
blocks from my house.
30. A rectangle has an area of 63ft2. Its width is 2 ft less than its length. What are the dimensions of the rectangle?
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