13. Multiply the following polynomials and simplify:
(2x5 + x3)(10x5 + x3 - 4)
20x10 + 12x8 + x6 - 8x5 - 4x3
(2x5 + 4x4 + 8x)(5x2 + 4x - 6)
10x7 + 28x6 + 4x5 - 24x4 + 40x3 + 32x2 - 48x
14. Divide:
4x3 + 10x2 + 12x + 30 / 2x + 5
2x2 + 6
15. Find the greatest common factor of the following terms:
36, 54
18
30y9, 39x2y6
3y6
16. Factor the following polynomials:
12x4 - 35x3 - 68x2
12x2(x +
4
3
)(x -
17
4
)
x2 - x - 20
(x + 4)(x - 5)
x5 + 22x4 + 117x3
x3(x + 13)(x + 9)
17. For question 16, exercises b) and c), solve for x:
x =
-4
and
5
x =
0
,
-13
and
-9
18. You have 5 CDs. How many different ways can you listen to them?
120
19. Use the following data to construct a box and whiskers plot:
33, 1, 36, 32, 30, 38, 5, 22
20. A bag contains 2 blue balls, 3 red balls, and 3 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
37.50%
A blue ball or red ball?
62.50%
Two red balls?
14.06%
A blue ball and a white ball?
9.38%
21. Solve and graph the following systems of linear equations:
x + y = 1 x - y = -9
A(-4,5)
5x - 6y = -10 5x + 2y = -14
B(-2.6,-0.5)
22. Write the following fractions in simplest form:
18x10y6
36x8y4
x2y2
2
x8 + 6x7 - 7x6
x5(x - 1)
x(x + 7)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
14x = x2 + 45
x1 = 9, x2 = 5
24. Convert the following repeating decimal into a fraction:
x =
0.49
45
90
25. Solve the following equation:
6 +
x - 10
= 20
x = 206
26. Rationalize the denominator of each fraction below:
3
3
3
27. Use a trigonometric ratio to find x:
x = 21.94 cm
28. The sum of two consecutive even integers is 58. What are the integers? (Hint: use 2x as the first even integer)
a=28, b=30
29. After you leave your house, you walk 12 blocks west and 16 blocks south. How far are you from your house?
I am
20
blocks from my house.
30. The length of a rectangle is 5 less than 5 times the width. What are the dimensions of the rectangle if the area is 210ft2?
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