13. Multiply the following polynomials and simplify:
(4x + 10)(1x3 + 9)
4x4 + 10x3 + 36x + 90
(6x2 + 4x - 6)(7x4 - 9)
42x6 + 28x5 - 42x4 - 54x2 - 36x + 54
14. Divide:
2x3 - 3x2 - 10x + 15 / 2x - 3
x2 - 5
15. Find the greatest common factor of the following terms:
42, 90
6
18x5y9, 54x6y10
18x5y9
16. Factor the following polynomials:
x4 + 27x3 + 72x2
x2(x + 3)(x + 24)
x2 + 18x + 80
(x + 10)(x + 8)
x7 - 21x6 + 98x5
x5(x - 14)(x - 7)
17. For question 16, exercises b) and c), solve for x:
x =
-10
and
-8
x =
0
,
14
and
7
18. How many ways can 6 people wait in line?
720
19. Use the following data to construct a box and whiskers plot:
1, 25, 38, 35, 18, 39, 13, 11
20. A bag contains 7 blue balls, 3 red balls, and 7 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
41.18%
A blue ball or red ball?
58.82%
Two red balls?
3.11%
A blue ball and a white ball?
16.96%
21. Solve and graph the following systems of linear equations:
x + y = 1 x - y = -18
A(-8.5,9.5)
2x - 8y = 18 6x + 10y = 10
B(3.82,-1.29)
22. Write the following fractions in simplest form:
20x4y4
60x7y4
1
3x3
x8 + 7x7 - 30x6
x5(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 - 37x = 78
x1 = 39, x2 = -2
24. Convert the following repeating decimal into a fraction:
x =
0.2759
2732
9900
25. Solve the following equation:
14
x
= 5
x =
196
25
26. Rationalize the denominator of each fraction below:
4
28
15
12
4
21
45
27. Use a trigonometric ratio to find x:
x = 35.36 cm
28. The sum of two consecutive even integers is 14. What are the integers? (Hint: use 2x as the first even integer)
a=6, b=8
29. After you leave your house, you walk 8 blocks east and 15 blocks south. How far are you from your house?
I am
17
blocks from my house.
30. Each side of a square is decreased by 9 m. The area of the newly created square is 121m2. What was the original length of one side of the square?
13. Multiply the following polynomials and simplify:
(10x5 + 4x2 + 10x)(7x4 + 7x - 3)
70x9 + 98x6 + 40x5 + 28x3 + 58x2 - 30x
(9x4 + 5x3 + 10)(5x3 + 7)
45x7 + 25x6 + 63x4 + 85x3 + 70
14. Divide:
9x2 + 18x - 16 / 3x - 2
3x + 8
15. Find the greatest common factor of the following terms:
60, 90, 11
1
96x5y5, 36xy9, 65x6y8
xy5
16. Factor the following polynomials:
56x4 + 0x3 - 14x2
56x2(x +
1
2
)(x -
1
2
)
x2 - 14x + 40
(x - 10)(x - 4)
x8 + 18x7 + 45x6
x6(x + 15)(x + 3)
17. For question 16, exercises b) and c), solve for x:
x =
10
and
4
x =
0
,
-15
and
-3
18. You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate or vanilla. How many choices do you have?
8
19. Use the following data to construct a box and whiskers plot:
8, 26, 15, 24, 2, 29, 11, 7, 5, 23
20. A bag contains 5 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?
41.67%
A blue ball or red ball?
58.33%
Two red balls?
1.52%
A blue ball and a white ball?
18.94%
21. Solve and graph the following systems of linear equations:
x + y = 7 x - y = -10
A(-1.5,8.5)
3x - 8y = -1 4x + 3y = -20
B(-3.98,-1.37)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x2 + 14x + 49)
(x + 7)
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 + x = 12
x1 = 3, x2 = -4
24. Convert the following repeating decimal into a fraction:
x =
9.131
9040
990
25. Solve the following equation:
-16 +
5x - 6
= 1
x = 59
26. Rationalize the denominator of each fraction below:
7
21 -
6
147 + 7
6
435
27. Use a trigonometric ratio to find x:
x = 21.00 cm
28. The sum of two consecutive even integers is 62. What are the integers? (Hint: use 2x as the first even integer)
a=30, b=32
29. After you leave your house, you walk 6 blocks north and 8 blocks west. How far are you from your house?
I am
10
blocks from my house.
30. A rectangle has an area of 20m2. Its width is 8 m less than its length. What are the dimensions of the rectangle?
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