13. Multiply the following polynomials and simplify:
-7(4x5 + x4 + 4x2)
-28x5 - 7x4 - 28x2
(4x5 + 2x3 + 8x)(9x3 + 5)
36x8 + 18x6 + 20x5 + 72x4 + 10x3 + 40x
14. Divide:
20x2 + 51x + 28 / 4x + 7
5x + 4
15. Find the greatest common factor of the following terms:
56, 100
4
45xy8, 50x9y6, 22x6y7
xy6
16. Factor the following polynomials:
8x5 - 15x4 - 2x3
8x3(x - 2)(x +
1
8
)
x2 - x - 90
(x + 9)(x - 10)
x5 - 15x4 + 56x3
x3(x - 8)(x - 7)
17. For question 16, exercises b) and c), solve for x:
x =
-9
and
10
x =
0
,
8
and
7
18. You have 4 pants, 4 shirts, and 3 shoes. How many different ways can you dress?
48
19. Use the following data to construct a box and whiskers plot:
23, 3, 21, 34, 7, 37, 27, 39, 22, 36
20. A bag contains 5 blue balls, 3 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?
20.00%
A blue ball or red ball?
80.00%
Two red balls?
6.67%
A blue ball and a white ball?
11.11%
21. Solve and graph the following systems of linear equations:
x + y = 18 x - y = -7
A(5.5,12.5)
9x - 10y = 10 2x + 9y = -11
B(-0.2,-1.18)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
x3 - 2x2 - 24x
x4(x + 4)
(x - 6)
x3
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
12x = x2 + 11
x1 = 1, x2 = 11
24. Convert the following repeating decimal into a fraction:
x =
0.531
531
999
25. Solve the following equation:
40
x
= 2
x = 10
26. Rationalize the denominator of each fraction below:
14
6 -
14
42 + 7
14
11
27. Use a trigonometric ratio to find x:
x = 9.81 cm
28. The sum of two consecutive even integers is 34. What are the integers? (Hint: use 2x as the first even integer)
a=16, b=18
29. After you leave your house, you walk 4 blocks east and 3 blocks north. How far are you from your house?
I am
5
blocks from my house.
30. A rectangle has an area of 7m2. Its width is 6 m less than its length. What are the dimensions of the rectangle?
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