13. Multiply the following polynomials and simplify:
(7x5 + 5x4)4x3
28x8 + 20x7
(4x4 + 2x3 + 6)(7x5 + 10)
28x9 + 14x8 + 42x5 + 40x4 + 20x3 + 60
14. Divide:
8x3 - 14x2 + 12x - 21 / 4x - 7
2x2 + 3
15. Find the greatest common factor of the following terms:
15, 36, 45
3
30x5y, 39x3, 22x3
x3
16. Factor the following polynomials:
20x3 + 16x2 + 1x
20x(x -
-4 +
11
10
)(x -
-4 -
11
10
)
x2 - 17x + 70
(x - 7)(x - 10)
x8 - 8x7 + 12x6
x6(x - 2)(x - 6)
17. For question 16, exercises b) and c), solve for x:
x =
7
and
10
x =
0
,
2
and
6
18. You have 6 books to read. How many different ways can you read your books?
720
19. Use the following data to construct a box and whiskers plot:
37, 24, 23, 21, 18, 30, 36, 32
20. A bag contains 2 blue balls, 7 red balls, and 2 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
18.18%
A blue ball or red ball?
81.82%
Two red balls?
38.18%
A blue ball and a white ball?
3.64%
21. Solve and graph the following systems of linear equations:
x + y = 10 x - y = 19
A(14.5,-4.5)
10x - 2y = -2 2x + y = -14
B(-2.14,-9.71)
22. Write the following fractions in simplest form:
5x7y2
15x10y
y
3x3
(x2 - 2x + 1)
(x - 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.
-15 = x2 + 16x
x1 = -1, x2 = -15
24. Convert the following repeating decimal into a fraction:
x =
0.39
39
99
25. Solve the following equation:
-17
x
- 10 = -20
x
+ 8
x = 36
26. Rationalize the denominator of each fraction below:
10
2 -
10
-
10 + 5
10
3
27. Use a trigonometric ratio to find x:
x = 16.50 cm
28. The sum of two consecutive even integers is 46. What are the integers? (Hint: use 2x as the first even integer)
a=22, b=24
29. After you leave your house, you walk 3 blocks east and 4 blocks north. How far are you from your house?
I am
5
blocks from my house.
30. Each side of a square is lengthened by 3 ft. This makes the area of the square 361ft2. What is the original length of a side of the square?