13. Multiply the following polynomials and simplify:
(2x5 + 6x)2x3
4x8 + 12x4
(3x3 + 3x2 + 2x)(9x4 + 3x + 3)
27x7 + 27x6 + 18x5 + 9x4 + 18x3 + 15x2 + 6x
14. Divide:
8x2 + 26x - 45 / 4x - 5
2x + 9
15. Find the greatest common factor of the following terms:
375, 180
15
450y8, 65x9y4, 336y4
y4
16. Factor the following polynomials:
30x3 - 12x2 + 1x
30x(x -
6 +
6
30
)(x -
6 -
6
30
)
x2 - 4x - 5
(x - 5)(x + 1)
x5 - 8x4 + 7x3
x3(x - 7)(x - 1)
17. For question 16, exercises b) and c), solve for x:
x =
5
and
-1
x =
0
,
7
and
1
18. You have 2 pants, 3 shirts, and 2 shoes. How many different ways can you dress?
12
19. Use the following data to construct a box and whiskers plot:
18, 6, 21, 31, 30, 8, 29, 14, 20, 22
20. A bag contains 3 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?
25.00%
A blue ball or red ball?
75.00%
Two red balls?
22.73%
A blue ball and a white ball?
6.82%
21. Solve and graph the following systems of linear equations:
x + y = 17 x - y = 10
A(13.5,3.5)
7x - 8y = -20 4x + 8y = -4
B(-2.18,0.59)
22. Write the following fractions in simplest form:
14x10y
42x9y
x
3
(x + 2)2
(x + 2)5
1
(x + 2)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 = -4x - 12
x1 = -2, x2 = 6
24. Convert the following repeating decimal into a fraction:
x =
0.573
5680
9900
25. Solve the following equation:
-3
x
- 3 = -6
x
+ 15
x = 36
26. Rationalize the denominator of each fraction below:
6
21
+ 3
21
- 3
2
27. Use a trigonometric ratio to find x:
x = 16.17 cm
28. The sum of two consecutive odd integers is 40. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=19, b=21
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 width that is 3 m less than its length. The area of the rectangle is 180m2. What are the dimensions of the rectangle?
13. Multiply the following polynomials and simplify:
3x5(7x5 + 6x2 + 6x)
21x10 + 18x7 + 18x6
(1x5 + 4x4 + 5)(1x5 + 3x4)
x10 + 7x9 + 12x8 + 5x5 + 15x4
14. Divide:
8x2 - 28x + 22 / 2x - 5
(4x - 4) with a remainder of 2
15. Find the greatest common factor of the following terms:
270, 120
30
468x5y6, 180x6y3
36x5y3
16. Factor the following polynomials:
18x4 + 10x3 + 1x2
18x2(x -
-5 +
7
18
)(x -
-5 -
7
18
)
x2 + 9x - 10
(x - 1)(x + 10)
x4 + 0x3 - 25x2
x2(x + 5)(x - 5)
17. For question 16, exercises b) and c), solve for x:
x =
1
and
-10
x =
0
,
-5
and
5
18. You are seating 7 people on 7 chairs. How many different ways can those people sit?
5040
19. Use the following data to construct a box and whiskers plot:
23, 21, 26, 17, 34, 37, 7
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 = 2 x - y = -11
A(-4.5,6.5)
5x - 10y = -10 8x + y = 4
B(0.35,1.18)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
(x + 1)5
(x + 1)6
1
x + 1
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x2 + 2x = 3
x1 = -3, x2 = 1
24. Convert the following repeating decimal into a fraction:
x =
6.41
577
90
25. Solve the following equation:
5
x
- 18 = 4
x
+ 10
x = 784
26. Rationalize the denominator of each fraction below:
10
6
- 6
-
6
+ 6
3
27. Use a trigonometric ratio to find x:
x = 13.86 cm
28. The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28
29. After you leave your house, you walk 12 blocks east and 9 blocks south. How far are you from your house?
I am
15
blocks from my house.
30. A rectangle has an area of 228m2. Its width is 7 m less than its length. What are the dimensions of the rectangle?
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