13. Multiply the following polynomials and simplify:
(4x5 + 6x4)(7x5 + 10x3)
28x10 + 42x9 + 40x8 + 60x7
(8x2 + 4x)(1x5 + 5x2 + x)
8x7 + 4x6 + 40x4 + 28x3 + 4x2
14. Divide:
6x2 - 8x + 10 / 2x - 4
(3x + 2) with a remainder of 18
15. Find the greatest common factor of the following terms:
48, 30, 70
2
33x7y3, 77x7y8, 27xy6
xy3
16. Factor the following polynomials:
45x3 + 21x2 - 24x
45x(x -
8
15
)(x + 1)
x2 + 0x - 36
(x + 6)(x - 6)
x5 + 8x4 - 20x3
x3(x - 2)(x + 10)
17. For question 16, exercises b) and c), solve for x:
x =
-6
and
6
x =
0
,
2
and
-10
18. You have 4 pants, 5 shirts, and 5 shoes. How many different ways can you dress?
100
19. Use the following data to construct a box and whiskers plot:
4, 32, 17, 21, 33, 29, 36, 26, 22
20. A bag contains 3 blue balls, 5 red balls, and 4 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:
A white ball?
33.33%
A blue ball or red ball?
66.67%
Two red balls?
15.15%
A blue ball and a white ball?
9.09%
21. Solve and graph the following systems of linear equations:
x + y = -14 x - y = 6
A(-4,-10)
3x - 4y = 7 10x + 3y = 5
B(0.84,-1.12)
22. Write the following fractions in simplest form:
14x10y4
7x7y5
2x3
y
x(x - 1)
x5 - 6x4 + 5x3
1
x2(x - 5)
23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
16x + 15 = -x2
x1 = -15, x2 = -1
24. Convert the following repeating decimal into a fraction:
x =
0.6
6
9
25. Solve the following equation:
6 -
5x + 10
= -9
x = 43
26. Rationalize the denominator of each fraction below:
49
14
- 6
-
49
14
+ 294
22
27. Use a trigonometric ratio to find x:
x = 15.00 cm
28. The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=17, b=19
29. After you leave your house, you walk 12 blocks north and 9 blocks west. How far are you from your house?
I am
15
blocks from my house.
30. A rectangle has a width that is 4 m less than its length. The area of the rectangle is 21m2. What are the dimensions of the rectangle?