15. Find the greatest common factor of the following terms:

54, 42

6

40x^{8}y^{5}, 35x^{3}y^{2}

5x^{3}y^{2}

16. Factor the following polynomials:

32x^{4} + 66x^{3} + 4x^{2}

32x^{2}(x +

1

16

)(x + 2)

x^{2} - 2x - 15

(x - 5)(x + 3)

x^{6} - 15x^{5} + 14x^{4}

x^{4}(x - 14)(x - 1)

17. For question 16, exercises b) and c), solve for x:

x =

5

and

-3

x =

0

,

14

and

1

18. You have 8 books to read. How many different ways can you read your books?

40320

19. Use the following data to construct a box and whiskers plot:

23, 24, 11, 33, 15, 35, 16, 27, 13

20. Suppose you toss a coin and spin a spinner numbered 1 through 13

What is the probability of getting tails and 2?

3.85%

What is the probability of getting tails and an odd number?

23.08%

What is the probability of getting tails and a multiple of 2?

23.08%

What is the probability of getting heads and a prime number?

23.08%

What is the probability of not tails and not 3?

46.15%

What is the probability of getting not heads 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 tails?

50%

21. Solve and graph the following systems of linear equations:

x + y = -17 x - y = 8

A(-4.5,-12.5)

x - 2y = -12 x + 8y = -14

B(-12.4,-0.2)

22. Write the following fractions in simplest form:

6x^{10}y^{5}

3xy^{6}

2x^{9}

y

x^{3} + 1x^{2} - 72x

x^{5}(x - 8)

(x + 9)

x^{4}

23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.

8x + 7 = -x^{2}

x_{1} = -7, x_{2} = -1

24. Convert the following repeating decimal into a fraction:

x =
0.915

915

999

25. Solve the following equation:

2x + 5

- 6 = 9

x = 110

26. Rationalize the denominator of each fraction below:

21

3

21 +

2

441

3

- 21

6

439

27. Use a trigonometric ratio to find x:

x = 25.46 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 15 blocks north and 8 blocks east. How far are you from your house?

I am

17

blocks from my house.

30. Each side of a square is decreased by 2 ft. The area of the newly created square is 25ft^{2}. What was the original length of one side of the square?