13. Multiply the following polynomials and simplify:
(8x4 + 4x2 + x)(7x5 + 4x3 + 6)
56x9 + 60x7 + 7x6 + 16x5 + 52x4 + 24x2 + 6x
(10x3 + 2)(5x5 + 5x4 + 10x2)
50x8 + 50x7 + 110x5 + 10x4 + 20x2
14. Divide:
10x2 + x - 2 / 5x - 2
2x + 1
15. Find the greatest common factor of the following terms:
70, 54, 30
2
24x8y6, 72y, 60x4y2
12y
16. Factor the following polynomials:
25x5 - 100x4 + 51x3
25x3(x -
3
5
)(x -
17
5
)
x2 + 8x - 9
(x - 1)(x + 9)
x5 + x4 - 72x3
x3(x + 9)(x - 8)
17. For question 16, exercises b) and c), solve for x:
x =
1
and
-9
x =
0
,
-9
and
8
18. You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate or vanilla. How many choices do you have?
12
19. Use the following data to construct a box and whiskers plot:
30, 3, 38, 21, 39, 9, 24
20. Suppose you toss a coin and spin a spinner numbered 1 through 17
What is the probability of getting tails and 10?
2.94%
What is the probability of getting tails and an odd number?
23.53%
What is the probability of getting tails and a multiple of 5?
8.82%
What is the probability of getting tails and a prime number?
20.59%
What is the probability of not heads and not 13?
47.06%
What is the probability of getting not tails and not a whole number?
0%
What is the probability of heads or tails and a whole number?
100%
What is the probability of getting heads?
50%
21. Solve and graph the following systems of linear equations:
x + y = -12 x - y = -11
A(-11.5,-0.5)
x - 7y = -1 2x + 8y = -20
B(-6.73,-0.82)
22. Write the following fractions in simplest form:
22x6y7z4
44x7y9z2
z2
2xy2
x4(x + 6)
x7 + 9x6 + 18x5
1
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 - 90 = 9x
x1 = 15, x2 = -6
24. Convert the following repeating decimal into a fraction:
x =
0.32
290
900
25. Solve the following equation:
4 -
2x - 7
= -7
x = 64
26. Rationalize the denominator of each fraction below:
2
10
2
6
15
3
27. Use a trigonometric ratio to find x:
x = 20.78 cm
28. The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=25, b=27
29. After you leave your house, you walk 6 blocks east and 8 blocks north. How far are you from your house?
I am
10
blocks from my house.
30. A rectangle has a length 10 ft greater than its width. The area of the rectangle is 375ft2. What are the length and width of the rectangle?
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