13. Multiply the following polynomials and simplify:
(1x3 + 9x2 + 9x)10x
10x4 + 90x3 + 90x2
(1x5 + 4x2 + 8x)(3x5 + 9x4)
3x10 + 9x9 + 12x7 + 60x6 + 72x5
14. Divide:
8x3 + 10x2 - 8x - 10 / 4x + 5
2x2 - 2
15. Find the greatest common factor of the following terms:
56, 90, 78
2
9x6y5, 54x9y6
9x6y5
16. Factor the following polynomials:
8x4 + 10x3 - 42x2
8x2(x -
7
4
)(x + 3)
x2 - 8x - 20
(x - 10)(x + 2)
x8 - 21x7 + 110x6
x6(x - 11)(x - 10)
17. For question 16, exercises b) and c), solve for x:
x =
10
and
-2
x =
0
,
11
and
10
18. You are seating 4 people on 4 chairs. How many different ways can those people sit?
24
19. Use the following data to construct a box and whiskers plot:
8, 26, 22, 29, 16, 21, 31
20. A bag contains 4 blue balls, 5 red balls, and 6 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
40.00%
A blue ball or red ball?
60.00%
Two red balls?
9.52%
A blue ball and a white ball?
11.43%
21. Solve and graph the following systems of linear equations:
x + y = -3 x - y = -4
A(-3.5,0.5)
x - 3y = -4 10x + 4y = -13
B(-1.62,0.79)
22. Write the following fractions in simplest form:
17x10y3
34x4y4
x6
2y
(x - 8)4
(x - 8)3
x - 8
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
-x2 = 6x - 7
x1 = 1, x2 = -7
24. Convert the following repeating decimal into a fraction:
x =
0.75
75
99
25. Solve the following equation:
-3
x
- 2 = -1
x
- 12
x = 25
26. Rationalize the denominator of each fraction below:
7
3
9 +
15
21
3
- 7
5
22
27. Use a trigonometric ratio to find x:
x = 17.68 cm
28. The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14
29. After you leave your house, you walk 9 blocks east and 12 blocks north. How far are you from your house?
I am
15
blocks from my house.
30. A rectangle has a length 8 ft greater than its width. The area of the rectangle is 33ft2. What are the length and width of the rectangle?
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