13. Multiply the following polynomials and simplify:
(7x5 + 6x3 + 6x2)5x3
35x8 + 30x6 + 30x5
(3x4 + 8x + 3)(10x4 + 6x2 + 9x)
30x8 + 18x6 + 107x5 + 30x4 + 48x3 + 90x2 + 27x
14. Divide:
6x2 - 19x + 10 / 3x - 2
2x - 5
15. Find the greatest common factor of the following terms:
90, 84
6
70x3y9, 56x, 45x2y10
x
16. Factor the following polynomials:
5x4 - 5x3 - 30x2
5x2(x + 2)(x - 3)
x2 - 2x - 24
(x + 4)(x - 6)
x6 - 26x5 + 165x4
x4(x - 15)(x - 11)
17. For question 16, exercises b) and c), solve for x:
x =
-4
and
6
x =
0
,
15
and
11
18. You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate, vanilla, strawberry, peach or kiwi. How many choices do you have?
20
19. Use the following data to construct a box and whiskers plot:
39, 14, 13, 1, 8, 26, 15
20. A bag contains 2 blue balls, 7 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?
40.00%
A blue ball or red ball?
60.00%
Two red balls?
21.78%
A blue ball and a white ball?
5.33%
21. Solve and graph the following systems of linear equations:
x + y = 12 x - y = 17
A(14.5,-2.5)
x - 5y = -20 9x + 5y = -9
B(-2.9,3.42)
22. Write the following fractions in simplest form:
24xy2
12x7y3
2
x6y
(x + 5)3
(x + 5)2
x + 5
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
-8x = x2 + 7
x1 = -7, x2 = -1
24. Convert the following repeating decimal into a fraction:
x =
0.36
33
90
25. Solve the following equation:
20
x
= 2
x = 5
26. Rationalize the denominator of each fraction below:
14
6
7
6
3
27. Use a trigonometric ratio to find x:
x = 32.91 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. A rectangle has a width that is 5 ft less than its length. The area of the rectangle is 336ft2. What are the dimensions of the rectangle?
13. Multiply the following polynomials and simplify:
(10x3 + 8x2 + 3x)(2x5 + 6x)
20x8 + 16x7 + 6x6 + 60x4 + 48x3 + 18x2
(7x5 + 4x4)(2x4 + x3)
14x9 + 15x8 + 4x7
14. Divide:
3x2 - 17x - 81 / 3x + 10
(x - 9) with a remainder of 9
15. Find the greatest common factor of the following terms:
20, 54
2
22x6y, 91y10, 18y8
y
16. Factor the following polynomials:
8x3 - x2 - 9x
8x(x -
9
8
)(x + 1)
x2 - 3x - 70
(x + 7)(x - 10)
x8 + 5x7 - 14x6
x6(x + 7)(x - 2)
17. For question 16, exercises b) and c), solve for x:
x =
-7
and
10
x =
0
,
-7
and
2
18. You can purchase your ice cream in a cup or a cone. Orders can be one, two, three, or four scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
32
19. Use the following data to construct a box and whiskers plot:
18, 12, 25, 31, 3, 40, 34, 7
20. A bag contains 2 blue balls, 2 red balls, and 4 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?
6.25%
A blue ball and a white ball?
12.50%
21. Solve and graph the following systems of linear equations:
x + y = -3 x - y = -13
A(-8,5)
7x - y = 9 6x + 6y = -6
B(1,-2)
22. Write the following fractions in simplest form:
18xy
36x2y5
1
2xy4
(x - 6)4
(x - 6)6
1
(x - 6)2
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x2 - 4x = 21
x1 = 7, x2 = -3
24. Convert the following repeating decimal into a fraction:
x =
0.7
7
9
25. Solve the following equation:
-
4x + 4
- 1 = -19
x = 80
26. Rationalize the denominator of each fraction below:
10
5
- 15
-
5
+ 15
22
27. Use a trigonometric ratio to find x:
x = 9.81 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 south and 16 blocks east. How far are you from your house?
I am
20
blocks from my house.
30. Each side of a square is decreased by 8 m. The area of the newly created square is 64m2. What was the original length of one side of the square?
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