13. Multiply the following polynomials and simplify:
(8x2 + 4x + 9)4x4
32x6 + 16x5 + 36x4
(4x - 1)(9x3 + 9x2)
36x4 + 27x3 - 9x2
14. Divide:
6x2 - 42x + 72 / 3x - 9
2x - 8
15. Find the greatest common factor of the following terms:
55, 22, 75
1
90y8, 15x4y4
15y4
16. Factor the following polynomials:
3x3 - 27x2 - 66x
3x(x + 2)(x - 11)
x2 - 4x - 5
(x + 1)(x - 5)
x8 - 12x7 - 45x6
x6(x - 15)(x + 3)
17. For question 16, exercises b) and c), solve for x:
x =
-1
and
5
x =
0
,
15
and
-3
18. How many ways can 3 people wait in line?
6
19. Use the following data to construct a box and whiskers plot:
18, 33, 14, 2, 11, 22, 34
20. A bag contains 6 blue balls, 5 red balls, and 6 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
35.29%
A blue ball or red ball?
64.71%
Two red balls?
8.65%
A blue ball and a white ball?
12.46%
21. Solve and graph the following systems of linear equations:
x + y = 14 x - y = -10
A(2,12)
10x - 2y = -9 6x + y = -17
B(-1.95,-5.27)
22. Write the following fractions in simplest form:
16x7y7
64x5y7
x2
4
x4 + 9x3 - 10x2
x(x - 1)
x(x + 10)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
2x = x2 - 8
x1 = 4, x2 = -2
24. Convert the following repeating decimal into a fraction:
x =
0.30
30
99
25. Solve the following equation:
x - 9
- 16 = -16
x = 9
26. Rationalize the denominator of each fraction below:
5
14 +
7
70 - 5
7
189
27. Use a trigonometric ratio to find x:
x = 28.87 cm
28. The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=25, b=27
29. After you leave your house, you walk 6 blocks west and 8 blocks south. How far are you from your house?
I am
10
blocks from my house.
30. A rectangle has an area of 54ft2. Its width is 3 ft less than its length. What are the dimensions of the rectangle?
13. Multiply the following polynomials and simplify:
4x(9x5 + 8x4 - 10)
36x6 + 32x5 - 40x
(2x2 - 5)(2x2 + 6x - 3)
4x4 + 12x3 - 16x2 - 30x + 15
14. Divide:
10x3 + 18x2 + 5x + 9 / 5x + 9
2x2 + 1
15. Find the greatest common factor of the following terms:
66, 80
2
70x2y2, 72x7y5
2x2y2
16. Factor the following polynomials:
28x5 + 35x4 - 63x3
28x3(x +
9
4
)(x - 1)
x2 - 14x + 40
(x - 4)(x - 10)
x5 + 8x4 - 105x3
x3(x - 7)(x + 15)
17. For question 16, exercises b) and c), solve for x:
x =
4
and
10
x =
0
,
7
and
-15
18. You have 4 books to read. How many different ways can you read your books?
24
19. Use the following data to construct a box and whiskers plot:
17, 36, 23, 24, 34, 26, 35, 7, 14, 6
20. A bag contains 5 blue balls, 4 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?
35.71%
A blue ball or red ball?
64.29%
Two red balls?
8.16%
A blue ball and a white ball?
12.76%
21. Solve and graph the following systems of linear equations:
x + y = -7 x - y = 9
A(1,-8)
14x - 6y = 18 x + y = 17
B(6,11)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x2 + 12x + 36)
(x + 6)
x + 6
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x2 - 66 = 31x
x1 = 33, x2 = -2
24. Convert the following repeating decimal into a fraction:
x =
8.673
7806
900
25. Solve the following equation:
-5
x
+ 6 = -7
x
+ 16
x = 25
26. Rationalize the denominator of each fraction below:
10
2
+ 14
-
5
2
- 70
97
27. Use a trigonometric ratio to find x:
x = 17.68 cm
28. The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)
a=14, b=16
29. After you leave your house, you walk 5 blocks west and 12 blocks south. How far are you from your house?
I am
13
blocks from my house.
30. A rectangle has a length 10 ft greater than its width. The area of the rectangle is 264ft2. What are the length and width of the rectangle?
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