15. Find the greatest common factor of the following terms:
375, 180
15
450y^{8}, 65x^{9}y^{4}, 336y^{4}
y^{4}
16. Factor the following polynomials:
30x^{3}  12x^{2} + 1x
30x(x 
6 +
6
30
)(x 
6 
6
30
)
x^{2}  4x  5
(x  5)(x + 1)
x^{5}  8x^{4} + 7x^{3}
x^{3}(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:
14x^{10}y
42x^{9}y
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.
x^{2} = 4x  12
x_{1} = 2, x_{2} = 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 180m^{2}. What are the dimensions of the rectangle?
13. Multiply the following polynomials and simplify:
3x^{5}(7x^{5} + 6x^{2} + 6x)
21x^{10} + 18x^{7} + 18x^{6}
(1x^{5} + 4x^{4} + 5)(1x^{5} + 3x^{4})
x^{10} + 7x^{9} + 12x^{8} + 5x^{5} + 15x^{4}
14. Divide:
8x^{2}  28x + 22 / 2x  5
(4x  4) with a remainder of 2
15. Find the greatest common factor of the following terms:
270, 120
30
468x^{5}y^{6}, 180x^{6}y^{3}
36x^{5}y^{3}
16. Factor the following polynomials:
18x^{4} + 10x^{3} + 1x^{2}
18x^{2}(x 
5 +
7
18
)(x 
5 
7
18
)
x^{2} + 9x  10
(x  1)(x + 10)
x^{4} + 0x^{3}  25x^{2}
x^{2}(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:
22x^{6}y^{7}z^{4}
44x^{7}y^{9}z^{2}
z^{2}
2xy^{2}
(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.
x^{2} + 2x = 3
x_{1} = 3, x_{2} = 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 228m^{2}. Its width is 7 m less than its length. What are the dimensions of the rectangle?
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