13. Multiply the following polynomials and simplify:
-1(9x4 + 5x3)
-9x4 - 5x3
(2x5 + 8x2 + 8)(8x - 5)
16x6 - 10x5 + 64x3 - 40x2 + 64x - 40
14. Divide:
6x2 - 17x - 40 / 3x + 5
(2x - 9) with a remainder of 5
15. Find the greatest common factor of the following terms:
98, 42, 90
2
27xy6, 45x9y5
9xy5
16. Factor the following polynomials:
68x4 - 82x3 - 30x2
68x2(x +
5
17
)(x -
3
2
)
x2 - 4x - 60
(x + 6)(x - 10)
x5 - 9x4 - 52x3
x3(x + 4)(x - 13)
17. For question 16, exercises b) and c), solve for x:
x =
-6
and
10
x =
0
,
-4
and
13
18. How many ways can 5 people wait in line?
120
19. Use the following data to construct a box and whiskers plot:
14, 35, 13, 5, 10, 12, 7, 16, 40, 36
20. A bag contains 4 blue balls, 2 red balls, and 5 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
45.45%
A blue ball or red ball?
54.55%
Two red balls?
1.82%
A blue ball and a white ball?
18.18%
21. Solve and graph the following systems of linear equations:
x + y = -20 x - y = 1
A(-9.5,-10.5)
7x - 9y = 3 6x + 3y = -10
B(-1.08,-1.17)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x - 7)3
(x - 7)4
1
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.
x2 + 78 = 29x
x1 = 3, x2 = 26
24. Convert the following repeating decimal into a fraction:
x =
0.383
345
900
25. Solve the following equation:
32
x
= 4
x = 2
26. Rationalize the denominator of each fraction below:
2
21
5 +
3
5
21
- 3
7
11
27. Use a trigonometric ratio to find x:
x = 48.00 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 12 blocks east and 9 blocks north. How far are you from your house?
I am
15
blocks from my house.
30. Each side of a square is decreased by 7 ft. The area of the newly created square is 1ft2. What was the original length of one side of the square?
13. Multiply the following polynomials and simplify:
4x3(9x2 - 7)
36x5 - 28x3
(2x2 + 8x - 7)(7x5 + 5x)
14x7 + 56x6 - 49x5 + 10x3 + 40x2 - 35x
14. Divide:
5x2 + 8x + 33 / 5x + 3
(x + 1) with a remainder of 30
15. Find the greatest common factor of the following terms:
99, 80
1
24x8, 65x8y2
x8
16. Factor the following polynomials:
8x3 + 56x2 + 80x
8x(x + 2)(x + 5)
x2 - 3x - 54
(x - 9)(x + 6)
x9 + 6x8 - 72x7
x7(x - 6)(x + 12)
17. For question 16, exercises b) and c), solve for x:
x =
9
and
-6
x =
0
,
6
and
-12
18. You have 4 pants, 3 shirts, and 2 shoes. How many different ways can you dress?
24
19. Use the following data to construct a box and whiskers plot:
16, 35, 39, 21, 17, 26, 22, 27, 40
20. A bag contains 5 blue balls, 6 red balls, and 3 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
21.43%
A blue ball or red ball?
78.57%
Two red balls?
16.48%
A blue ball and a white ball?
8.24%
21. Solve and graph the following systems of linear equations:
x + y = 16 x - y = -1
A(7.5,8.5)
3x - 7y = 3 5x + 3y = -17
B(-2.5,-1.5)
22. Write the following fractions in simplest form:
21x4y7
84x3y5
xy2
4
x6 - 13x5 + 30x4
x3(x - 10)
x(x - 3)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x2 - 54 = 3x
x1 = 9, x2 = -6
24. Convert the following repeating decimal into a fraction:
x =
0.908
908
999
25. Solve the following equation:
32
x
= 2
x = 8
26. Rationalize the denominator of each fraction below:
4
15
10
28
105
35
27. Use a trigonometric ratio to find x:
x = 32.53 cm
28. The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9
29. After you leave your house, you walk 6 blocks west and 8 blocks north. How far are you from your house?
I am
10
blocks from my house.
30. A rectangle has an area of 368ft2. Its width is 7 ft less than its length. What are the dimensions of the rectangle?
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