13. Multiply the following polynomials and simplify:
(5x4 + 6x)(6x4 + 6x3 + 3x)
30x8 + 30x7 + 51x5 + 36x4 + 18x2
(8x4 + 4x)(9x5 + 5x2 + 8x)
72x9 + 76x6 + 64x5 + 20x3 + 32x2
14. Divide:
20x2 - 78x + 70 / 4x - 10
5x - 7
15. Find the greatest common factor of the following terms:
18, 52
2
16xy2, 84xy9, 63x6y3
xy2
16. Factor the following polynomials:
60x3 + 91x2 - 15x
60x(x +
5
3
)(x -
3
20
)
x2 - 13x + 40
(x - 8)(x - 5)
x5 - x4 - 132x3
x3(x + 11)(x - 12)
17. For question 16, exercises b) and c), solve for x:
x =
8
and
5
x =
0
,
-11
and
12
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:
38, 1, 24, 13, 14, 36, 33
20. A bag contains 5 blue balls, 3 red balls, and 7 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
46.67%
A blue ball or red ball?
53.33%
Two red balls?
4.00%
A blue ball and a white ball?
15.56%
21. Solve and graph the following systems of linear equations:
x + y = -4 x - y = -19
A(-11.5,7.5)
7x - 3y = -5 8x + 10y = -7
B(-0.76,-0.1)
22. Write the following fractions in simplest form:
54x7y7
18x8y
3y6
x
(x + 1)4
(x + 1)3
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.
5x + 6 = -x2
x1 = -3, x2 = -2
24. Convert the following repeating decimal into a fraction:
x =
0.499
450
900
25. Solve the following equation:
-1 +
2x + 3
= 16
x = 143
26. Rationalize the denominator of each fraction below:
3
12
35
28
3
21
245
27. Use a trigonometric ratio to find x:
x = 28.28 cm
28. The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)
a=14, b=16
29. After you leave your house, you walk 8 blocks north and 15 blocks west. How far are you from your house?
I am
17
blocks from my house.
30. The length of a rectangle is 6 more than twice its width. The area of the rectangle is 56m2. What is the length and width of the rectangle?
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