13. Multiply the following polynomials and simplify:

(4x + 10)(1x^{3} + 9)

4x^{4} + 10x^{3} + 36x + 90

(6x^{2} + 4x - 6)(7x^{4} - 9)

42x^{6} + 28x^{5} - 42x^{4} - 54x^{2} - 36x + 54

14. Divide:

2x^{3} - 3x^{2} - 10x + 15 / 2x - 3

x^{2} - 5

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

42, 90

6

18x^{5}y^{9}, 54x^{6}y^{10}

18x^{5}y^{9}

16. Factor the following polynomials:

x^{4} + 27x^{3} + 72x^{2}

x^{2}(x + 3)(x + 24)

x^{2} + 18x + 80

(x + 10)(x + 8)

x^{7} - 21x^{6} + 98x^{5}

x^{5}(x - 14)(x - 7)

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

x =

-10

and

-8

x =

0

,

14

and

7

18. How many ways can 6 people wait in line?

720

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

1, 25, 38, 35, 18, 39, 13, 11

20. A bag contains 7 blue balls, 3 red balls, and 7 white balls. You pick a ball from the bag and return it to the bag. What is the probability of picking:

A white ball?

41.18%

A blue ball or red ball?

58.82%

Two red balls?

3.11%

A blue ball and a white ball?

16.96%

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

x + y = 1 x - y = -18

A(-8.5,9.5)

2x - 8y = 18 6x + 10y = 10

B(3.82,-1.29)

22. Write the following fractions in simplest form:

20x^{4}y^{4}

60x^{7}y^{4}

1

3x^{3}

x^{8} + 7x^{7} - 30x^{6}

x^{5}(x + 10)

x(x - 3)

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} - 37x = 78

x_{1} = 39, x_{2} = -2

24. Convert the following repeating decimal into a fraction:

x =
0.2759

2732

9900

25. Solve the following equation:

14

x

= 5

x =

196

25

26. Rationalize the denominator of each fraction below:

4

28

15

12

4

21

45

27. Use a trigonometric ratio to find x:

x = 35.36 cm

28. The sum of two consecutive even integers is 14. What are the integers? (Hint: use 2x as the first even integer)

a=6, b=8

29. After you leave your house, you walk 8 blocks east and 15 blocks south. How far are you from your house?

I am

17

blocks from my house.

30. Each side of a square is decreased by 9 m. The area of the newly created square is 121m^{2}. What was the original length of one side of the square?

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

60, 90, 11

1

96x^{5}y^{5}, 36xy^{9}, 65x^{6}y^{8}

xy^{5}

16. Factor the following polynomials:

56x^{4} + 0x^{3} - 14x^{2}

56x^{2}(x +

1

2

)(x -

1

2

)

x^{2} - 14x + 40

(x - 10)(x - 4)

x^{8} + 18x^{7} + 45x^{6}

x^{6}(x + 15)(x + 3)

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

x =

10

and

4

x =

0

,

-15

and

-3

18. You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate or vanilla. How many choices do you have?

8

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

8, 26, 15, 24, 2, 29, 11, 7, 5, 23

20. A bag contains 5 blue balls, 2 red balls, and 5 white balls. You pick a ball from the bag and put it in your pocket. What is the probability of picking:

A white ball?

41.67%

A blue ball or red ball?

58.33%

Two red balls?

1.52%

A blue ball and a white ball?

18.94%

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

x + y = 7 x - y = -10

A(-1.5,8.5)

3x - 8y = -1 4x + 3y = -20

B(-3.98,-1.37)

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^{2} + 14x + 49)

(x + 7)

x + 7

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} + x = 12

x_{1} = 3, x_{2} = -4

24. Convert the following repeating decimal into a fraction:

x =
9.131

9040

990

25. Solve the following equation:

-16 +

5x - 6

= 1

x = 59

26. Rationalize the denominator of each fraction below:

7

21 -

6

147 + 7

6

435

27. Use a trigonometric ratio to find x:

x = 21.00 cm

28. The sum of two consecutive even integers is 62. What are the integers? (Hint: use 2x as the first even integer)

a=30, b=32

29. After you leave your house, you walk 6 blocks north and 8 blocks west. How far are you from your house?

I am

10

blocks from my house.

30. A rectangle has an area of 20m^{2}. Its width is 8 m less than its length. What are the dimensions of the rectangle?

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