13. Multiply the following polynomials and simplify:
10x3(2x3 + 7x + 8)
20x6 + 70x4 + 80x3
(1x3 + 7x2 + 10)(6x3 + 7x)
6x6 + 42x5 + 7x4 + 109x3 + 70x
14. Divide:
9x3 + 3x2 + 3x + 1 / 3x + 1
3x2 + 1
15. Find the greatest common factor of the following terms:
30, 91, 60
1
52x10y2, 18x6y9, 63xy4
xy2
16. Factor the following polynomials:
26x5 + 19x4 + 3x3
26x3(x +
3
13
)(x +
1
2
)
x2 + 4x - 60
(x + 10)(x - 6)
x9 + 9x8 - 70x7
x7(x - 5)(x + 14)
17. For question 16, exercises b) and c), solve for x:
x =
-10
and
6
x =
0
,
5
and
-14
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:
40, 24, 6, 20, 12, 27, 36
20. A bag contains 4 blue balls, 4 red balls, and 2 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
20.00%
A blue ball or red ball?
80.00%
Two red balls?
13.33%
A blue ball and a white ball?
8.89%
21. Solve and graph the following systems of linear equations:
x + y = 14 x - y = -1
A(6.5,7.5)
12x - 13y = -1 3x + 14y = 17
B(1,1)
22. Write the following fractions in simplest form:
66x6y3
22x7y6
3
xy3
(x - 7)7
(x - 7)4
(x - 7)3
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
65 = x2 - 8x
x1 = -5, x2 = 13
24. Convert the following repeating decimal into a fraction:
x =
0.348
345
990
25. Solve the following equation:
-8 -
x + 9
= -16
x = 55
26. Rationalize the denominator of each fraction below:
5
21 +
15
105 - 5
15
426
27. Use a trigonometric ratio to find x:
x = 21.21 cm
28. The sum of two consecutive even integers is 38. What are the integers? (Hint: use 2x as the first even integer)
a=18, b=20
29. After you leave your house, you walk 8 blocks west and 6 blocks south. How far are you from your house?
I am
10
blocks from my house.
30. A rectangle has a length 9 ft greater than its width. The area of the rectangle is 52ft2. What are the length and width of the rectangle?
13. Multiply the following polynomials and simplify:
4x3(8x5 + 2x3 + 6x)
32x8 + 8x6 + 24x4
(7x4 + 10x3 + 7x)(5x4 + 4)
35x8 + 50x7 + 35x5 + 28x4 + 40x3 + 28x
14. Divide:
6x2 + 7x - 20 / 2x + 5
3x - 4
15. Find the greatest common factor of the following terms:
42, 90, 18
6
63x8, 75x9y5, 22x7y9
x7
16. Factor the following polynomials:
20x4 + 80x3 + 55x2
20x2(x -
-4 +
5
2
)(x -
-4 -
5
2
)
x2 - 3x - 18
(x - 6)(x + 3)
x5 - x4 - 20x3
x3(x - 5)(x + 4)
17. For question 16, exercises b) and c), solve for x:
x =
6
and
-3
x =
0
,
5
and
-4
18. You are seating 6 people on 6 chairs. How many different ways can those people sit?
720
19. Use the following data to construct a box and whiskers plot:
35, 12, 14, 30, 33, 24, 32, 19, 25, 36
20. A bag contains 2 blue balls, 6 red balls, and 5 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
38.46%
A blue ball or red ball?
61.54%
Two red balls?
21.30%
A blue ball and a white ball?
5.92%
21. Solve and graph the following systems of linear equations:
x + y = -9 x - y = -5
A(-7,-2)
10x - 7y = 19 7x + 2y = 20
B(2.58,0.97)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
x(x + 10)
x8 + 3x7 - 70x6
1
x5(x - 7)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
12x = x2 - 13
x1 = 13, x2 = -1
24. Convert the following repeating decimal into a fraction:
x =
0.2437
2413
9900
25. Solve the following equation:
-
5x - 6
- 1 = -9
x = 14
26. Rationalize the denominator of each fraction below:
2
3 +
35
-
3 -
35
13
27. Use a trigonometric ratio to find x:
x = 26.00 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 12 blocks west and 9 blocks north. How far are you from your house?
I am
15
blocks from my house.
30. The sides of a square are increased by 8 ft. The area of the newly created square is 121ft2. What was the original length of one side of the square?
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