13. Multiply the following polynomials and simplify:
(10x5 + 3x2 + 10x)(3x5 + 7x4)
30x10 + 70x9 + 9x7 + 51x6 + 70x5
(9x3 + 4x + 10)(10x5 + x4 + 2)
90x8 + 9x7 + 40x6 + 104x5 + 10x4 + 18x3 + 8x + 20
14. Divide:
25x2 - 10x - 24 / 5x - 6
5x + 4
15. Find the greatest common factor of the following terms:
66, 45
3
60x3y10, 84x6y6, 22x3y7
2x3y6
16. Factor the following polynomials:
30x4 - 99x3 + 81x2
30x2(x -
3
2
)(x -
9
5
)
x2 + 3x - 54
(x - 6)(x + 9)
x8 + 9x7 - 22x6
x6(x + 11)(x - 2)
17. For question 16, exercises b) and c), solve for x:
x =
6
and
-9
x =
0
,
-11
and
2
18. You are seating 4 people on 4 chairs. How many different ways can those people sit?
24
19. Use the following data to construct a box and whiskers plot:
10, 35, 28, 8, 40, 19, 4
20. A bag contains 7 blue balls, 3 red balls, and 5 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:
A white ball?
33.33%
A blue ball or red ball?
66.67%
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 = 5 x - y = -6
A(-0.5,5.5)
2x - 10y = -12 12x + 14y = 2
B(-1,1)
22. Write the following fractions in simplest form:
27x5y8
9x7y4
3y4
x2
(x - 8)6
(x - 8)7
1
x - 8
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
x2 - 6 = -5x
x1 = 1, x2 = -6
24. Convert the following repeating decimal into a fraction:
x =
5.492
5438
990
25. Solve the following equation:
-
5x - 10
+ 10 = -5
x = 47
26. Rationalize the denominator of each fraction below:
7
18
7
2
6
27. Use a trigonometric ratio to find x:
x = 19.05 cm
28. The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15
29. After you leave your house, you walk 12 blocks south and 9 blocks west. How far are you from your house?
I am
15
blocks from my house.
30. The length of a rectangle is 6 less than 2 times the width. What are the dimensions of the rectangle if the area is 360ft2?