13. Multiply the following polynomials and simplify:

(1x^{4} + 5x^{3})1x^{3}

x^{7} + 5x^{6}

(4x^{5} - 4)(5x^{5} + 5x)

20x^{10} + 20x^{6} - 20x^{5} - 20x

14. Divide:

2x^{3} + 10x^{2} + 10x + 50 / 2x + 10

x^{2} + 5

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

75, 15

15

50x^{3}y^{3}, 52xy^{9}, 45x^{8}y^{8}

xy^{3}

16. Factor the following polynomials:

27x^{4} - 78x^{3} + 51x^{2}

27x^{2}(x - 1)(x -

17

9

)

x^{2} + 12x + 35

(x + 7)(x + 5)

x^{7} + 16x^{6} + 15x^{5}

x^{5}(x + 1)(x + 15)

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

x =

-7

and

-5

x =

0

,

-1

and

-15

18. You are seating 7 people on 7 chairs. How many different ways can those people sit?

5040

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

31, 7, 37, 20, 17, 29, 23

20. A bag contains 4 blue balls, 6 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?

16.00%

A blue ball and a white ball?

8.89%

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

x + y = 12 x - y = 14

A(13,-1)

3x - 9y = -20 5x + 7y = -10

B(-3.48,1.06)

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^{6} - 2x^{5} - 80x^{4}

x^{6}(x - 10)

(x + 8)

x^{2}

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

-x^{2} = -32x - 33

x_{1} = -1, x_{2} = 33

24. Convert the following repeating decimal into a fraction:

x =
0.138

137

990

25. Solve the following equation:

2 +

x + 10

= 16

x = 186

26. Rationalize the denominator of each fraction below:

3

14 +

35

42 - 3

35

161

27. Use a trigonometric ratio to find x:

x = 27.00 cm

28. The sum of two consecutive odd integers is 44. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=21, b=23

29. After you leave your house, you walk 3 blocks east and 4 blocks north. How far are you from your house?

I am

5

blocks from my house.

30. The length of a rectangle is 6 more than thrice its width. The area of the rectangle is 360m^{2}. What is the length and width of the rectangle?

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

78, 72

6

56x^{4}y^{3}, 36x^{3}y^{6}

4x^{3}y^{3}

16. Factor the following polynomials:

36x^{5} + 9x^{4} - 27x^{3}

36x^{3}(x + 1)(x -

3

4

)

x^{2} + 9x - 10

(x - 1)(x + 10)

x^{7} + 6x^{6} - 91x^{5}

x^{5}(x + 13)(x - 7)

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

x =

1

and

-10

x =

0

,

-13

and

7

18. How many ways can 5 people wait in line?

120

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

18, 26, 2, 39, 6, 29, 24

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 tails and an even number?

25%

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

25%

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

25%

What is the probability of not tails and not 2?

37.5%

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 heads?

50%

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

x + y = 7 x - y = 12

A(9.5,-2.5)

2x - y = -2 x + 9y = 18

B(0,2)

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 + 8)

(x^{2} + 16x + 64)

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.

19x + 70 = -x^{2}

x_{1} = -14, x_{2} = -5

24. Convert the following repeating decimal into a fraction:

x =
0.319

319

999

25. Solve the following equation:

-15

x

- 17 = -16

x

+ 19

x = 1296

26. Rationalize the denominator of each fraction below:

3

4 -

6

12 + 3

6

10

27. Use a trigonometric ratio to find x:

x = 20.78 cm

28. The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)

a=14, b=16

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

I am

13

blocks from my house.

30. Each side of a square is decreased by 3 ft. The area of the newly created square is 361ft^{2}. What was the original length of one side of the square?

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