13. Multiply the following polynomials and simplify:

8x^{5}(2x^{3} - 2)

16x^{8} - 16x^{5}

(3x^{5} + 10x^{4})(7x^{2} - 7)

21x^{7} + 70x^{6} - 21x^{5} - 70x^{4}

14. Divide:

15x^{3} - 12x^{2} - 15x + 20 / 5x - 4

(3x^{2} - 3) with a remainder of 8

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

49, 28, 100

1

33xy^{8}, 30y^{3}

3y^{3}

16. Factor the following polynomials:

14x^{4} + 12x^{3} - 2x^{2}

14x^{2}(x + 1)(x -

1

7

)

x^{2} - 5x - 24

(x - 8)(x + 3)

x^{4} + 18x^{3} + 65x^{2}

x^{2}(x + 5)(x + 13)

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

x =

8

and

-3

x =

0

,

-5

and

-13

18. You are seating 6 people on 6 chairs. How many different ways can those people sit?

720

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

6, 30, 3, 8, 19, 24, 16, 15, 5, 18

20. Suppose you toss a coin and spin a spinner numbered 1 through 4

What is the probability of getting tails and 1?

12.50%

What is the probability of getting heads and an even number?

25%

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

25%

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

25%

What is the probability of not heads and not 2?

37.5%

What is the probability of getting not tails 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 heads?

50%

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

x + y = 5 x - y = -2

A(1.5,3.5)

8x - 4y = -7 3x + 5y = 15

B(0.48,2.71)

22. Write the following fractions in simplest form:

16x^{10}y^{3}

8x^{4}y^{5}

2x^{6}

y^{2}

x^{3}(x + 9)

x^{3} + 3x^{2} - 54x

x^{2}

(x - 6)

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

-10 = x^{2} + 11x

x_{1} = -1, x_{2} = -10

24. Convert the following repeating decimal into a fraction:

x =
0.14

14

99

25. Solve the following equation:

11

x

- 20 = 2

x

- 2

x = 4

26. Rationalize the denominator of each fraction below:

35

20

7

5

2

27. Use a trigonometric ratio to find x:

x = 36.00 cm

28. The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=23, b=25

29. After you leave your house, you walk 12 blocks north and 5 blocks east. How far are you from your house?

I am

13

blocks from my house.

30. The sides of a square are increased by 10 ft. The area of the newly created square is 324ft^{2}. What was the original length of one side of the square?

13. Multiply the following polynomials and simplify:

(2x^{4} + 2x^{3} - 9)2x

4x^{5} + 4x^{4} - 18x

(6x - 3)(1x^{5} + 8x^{3} - 10)

6x^{6} - 3x^{5} + 48x^{4} - 24x^{3} - 60x + 30

14. Divide:

4x^{3} - 2x^{2} + 16x - 8 / 4x - 2

x^{2} + 4

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

49, 72, 75

1

50x^{5}y^{7}, 100x^{10}y

50x^{5}y

16. Factor the following polynomials:

56x^{3} + 32x^{2} + 4x

56x(x -

-4 +

2

14

)(x -

-4 -

2

14

)

x^{2} + 4x - 45

(x - 5)(x + 9)

x^{5} + 11x^{4} - 12x^{3}

x^{3}(x + 12)(x - 1)

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

x =

5

and

-9

x =

0

,

-12

and

1

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:

31, 34, 19, 20, 38, 28, 26, 21

20. A bag contains 4 blue balls, 3 red balls, and 2 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:

A white ball?

22.22%

A blue ball or red ball?

77.78%

Two red balls?

11.11%

A blue ball and a white ball?

9.88%

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

x + y = -7 x - y = 4

A(-1.5,-5.5)

x - 8y = -11 8x + 6y = 16

B(0.89,1.49)

22. Write the following fractions in simplest form:

22x^{6}y^{7}z^{4}

44x^{7}y^{9}z^{2}

z^{2}

2xy^{2}

x(x - 9)

x^{7} - 10x^{6} + 9x^{5}

1

x^{4}(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.

-10x = x^{2} - 75

x_{1} = -15, x_{2} = 5

24. Convert the following repeating decimal into a fraction:

x =
8.545

8460

990

25. Solve the following equation:

-6

x

+ 10 = -3

x

+ 7

x = 1

26. Rationalize the denominator of each fraction below:

35

9

35

3

27. Use a trigonometric ratio to find x:

x = 23.09 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 8 blocks north and 15 blocks west. How far are you from your house?

I am

17

blocks from my house.

30. A rectangle has a width that is 3 m less than its length. The area of the rectangle is 4m^{2}. What are the dimensions of the rectangle?

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