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1. Subtract.
6

x

3

3x + 8x

3

8x −
6

Choose the correct difference below.
A. 5x 6 − 9x 3
B. 11x 6 + 7x 3
C. 5x 6 − 7x 3
D. 5x 6 + 7x 3
2. Subtract.
2m3 −

5m2 + 10m +

3



2

− 13m + 10m −

4m −

The difference is 
(Simplify your answer.)

2
6

.

3. Perform the indicated operations.
2

2

2

2

7x − 7x − 57 + 2x + 9x
7x − 7x − 57 + 2x + 9x  =  
(Simplify your answer.)
4. Factor.
2

9y + 3y
2

9y + 3y =
(Factor completely.)
5. Factor.
4 2

3 3

4 2

3 3

4s t − 8s t

4s t − 8s t =
(Factor completely.)
6. Complete the factoring.
2








x   +  9x − 36
7. Write the rational expression in lowest terms.
2

y − 12y + 32
2

 

y + 3y − 28
2

y − 12y + 32

  =  
2
y + 3y − 28
(Simplify your answer.)

2

x   +  9x − 36  =   (x − 3 )(

 )

8. Add. Express your answer in lowest terms.
x+3
5x

+

4x + 8
2x

Choose the correct sum.
A.

13x + 31

B.

22x + 46

10x

C.

10x

9. Add as indicated. Express your answer in lowest terms.






3 + 3k 1 + k
+
4
8

D.

11x + 23
5x

5x + 11
7x

3 + 3k
4

+

1+k
8

=

10. Simplify.
50
Select the correct choice below and fill in any answer boxes within your choice.
A.

50 =
(Type an exact  answer, using radicals as  needed.)

B. The radical cannot be simplified.
11. Simplify the following radical.


Select the correct choice below and fill in any answer 
boxes within your choice.

1500
A. The radical cannot be simplified.
B. − 1500 =
 (Type an exact  answer, using radicals 
as  needed.)

12. Multiply and simplify by factoring.
5 14 • 7 10
5 14 • 7 10 =
(Type an exact  answer, using radicals as  needed.)
13. Solve.
x 2 − 19x + 90 = 0
Select the correct choice below and fill in any answer boxes within your choice.
A. The solutions are x =

(Use a comma to separate answers as needed.)
B. There is no real number solution.

14. Solve by completing the square.
2x 2 + 2x + 16 = 0

Select the correct choice below and fill in any answer 
boxes within your choice.
A. x  = 
 (Type an integer or a simplified fraction. 
Use a comma to separate answers as 
needed.)
B. There are no real solutions.

15. Solve by completing the square.
x 2 − 4x = − 3

Select the correct choice below  and, if  necessary, fill in the 
answer box to complete your choice.
A. The solutions are x  = 
.
 (Simplify your answers. Type an integer 
or a fraction. Use a comma to separate 
answers as  needed.)
B. There is no real solution.

1. A. 5x 6 − 9x 3

2. 15m3 − 15m2 + 14m + 8

3. 9x 2 + 2x − 57

4. 3y(3y + 1)

5. 4s 3 t2 (s − 2t)

6. x + 12

7. y − 8
y+7

8.

C. 

11x + 23
5x

9. 7(1 + k)
8

10. A.  50 =

11. B.  −

1500 =

5 2

 (Type an exact  answer, using radicals as  needed.)

− 10 15

 (Type an exact  answer, using radicals as needed.)

12. 70 35

13. A. The solutions are x =

9,10

.  (Use a comma to separate answers as  needed.)

14. B. There are no real solutions.

15. A. The solutions are x = 

1,3

.

(Simplify your answers. Type an integer or a fraction. Use a comma to separate answers as  needed.)


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