13. Multiply the following polynomials and simplify:

(4x^{4} + 5x^{2} + 7x)(9x^{5} + 3x^{3})

36x^{9} + 57x^{7} + 63x^{6} + 15x^{5} + 21x^{4}

(6x^{4} + 7x)(5x^{3} + 9x^{2} + 6)

30x^{7} + 54x^{6} + 71x^{4} + 63x^{3} + 42x

14. Divide:

10x^{2} - 45x + 35 / 5x - 5

2x - 7

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

78, 180, 60

6

147xy^{7}, 300y^{2}

3y^{2}

16. Factor the following polynomials:

6x^{3} - 14x^{2} + 6x

6x(x -

7 +

13

6

)(x -

7 -

13

6

)

x^{2} + 8x + 7

(x + 7)(x + 1)

x^{5} - 19x^{4} + 70x^{3}

x^{3}(x - 5)(x - 14)

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

x =

-7

and

-1

x =

0

,

5

and

14

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

20

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

16, 10, 25, 7, 22, 26, 27, 31, 20

20. A bag contains 6 blue balls, 4 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?

28.57%

A blue ball or red ball?

71.43%

Two red balls?

6.59%

A blue ball and a white ball?

13.19%

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

x + y = -20 x - y = -15

A(-17.5,-2.5)

5x - 9y = 17 6x + y = -6

B(-0.63,-2.24)

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 + 5)

(x^{2} + 10x + 25)

1

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.

14 = x^{2} + 5x

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

24. Convert the following repeating decimal into a fraction:

x =
0.5

5

9

25. Solve the following equation:

13

x

= 4

x =

169

16

26. Rationalize the denominator of each fraction below:

10

6

5 +

2

50

6

- 20

3

23

27. Use a trigonometric ratio to find x:

x = 15.59 cm

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

a=13, b=15

29. After you leave your house, you walk 12 blocks south 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 6 ft. The area of the newly created square is 361ft^{2}. What was the original length of one side of the square?

13. Multiply the following polynomials and simplify:

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

15x^{8} + 9x^{4}

(9x^{4} + 7)(4x^{4} + x)

36x^{8} + 9x^{5} + 28x^{4} + 7x

14. Divide:

20x^{2} - 45x + 25 / 4x - 5

5x - 5

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

200, 390

10

468x^{2}y^{8}, 264x^{6}y^{2}, 252x^{5}y^{3}

12x^{2}y^{2}

16. Factor the following polynomials:

21x^{5} - 21x^{4} - 42x^{3}

21x^{3}(x + 1)(x - 2)

x^{2} - 6x - 27

(x + 3)(x - 9)

x^{4} - 10x^{3} - 75x^{2}

x^{2}(x - 15)(x + 5)

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

x =

-3

and

9

x =

0

,

15

and

-5

18. You are seating 8 people on 8 chairs. How many different ways can those people sit?

40320

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

20, 25, 39, 21, 14, 11, 2

20. A bag contains 2 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?

38.46%

A blue ball or red ball?

61.54%

Two red balls?

21.30%

A blue ball and a white ball?

5.92%

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

x + y = -11 x - y = -10

A(-10.5,-0.5)

6x - 3y = 14 6x + 7y = 16

B(2.43,0.2)

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 - 1)^{6}

(x - 1)

(x - 1)^{5}

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

4x - 60 = -x^{2}

x_{1} = -10, x_{2} = 6

24. Convert the following repeating decimal into a fraction:

x =
0.35

35

99

25. Solve the following equation:

4

x

= 8

x =

16

64

26. Rationalize the denominator of each fraction below:

15

27

5

3

3

27. Use a trigonometric ratio to find x:

x = 13.28 cm

28. The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)

a=26, b=28

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

I am

13

blocks from my house.

30. The length of a rectangle is 10 less than 2 times the width. What are the dimensions of the rectangle if the area is 252ft^{2}?

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