I’ll be using the ^ symbol for exponents.
3 5 1
 
The solution is 6 (Simplify your answer, type an integer or
z z 3
fraction. Type N if there is no solution)
1. Solve:
2. Multiply. (5x  8)(3x 2  8x  5) The answer is 15x^3+64x^2+89x+40 (simplify your
answer)
3. Divide and simplify.
1
t4
= 9 (Type exponential notation with positive exponents)
13
t
t
4. Subtract. Simplify by collecting like radical terms if possible. 8 80  2 5 = 30 sqrt 5
(Simplify your answer. Type an exact answer, using radicals as needed.)
5. Solve. 25 x 4  25 x 2  6  0 The solution is x = _______ (Simplify your answer. Type
an exact answer, using radicals as needed. Rationalize all denominators. Use a comma
to separate answers as needed. Type N if there is no solution.)
sqrt 10 , - sqrt 10 , sqrt 15 , - sqrt 15
5
5
5
5
r 2  36
(r  6) 2
6. Simplify by removing factors of 1.
The simplified form is
r-6
r+6
7. Use rational exponents to simplify.
5
x15 = x^3 (Simplify your answer.)
8. Express using a positive exponent. d 9 = ______ (Simplify your answer. Type a
positive exponent.)
1
d^9
9. Subtract the polynomials. (13w 2  6w  2)  (6w 2  2) = -19w^2+6w (Simplify your
answer.)
10. Solve. ( x  7)( x  20)( x  4) > 0 The solution set is {x/ -7 < x < -4 or x > 20} (Use at
least one inequality or compound inequality to express your answer. For answers with
more than one inequality, separate the inequalities by a comma or the word ‘or’. Type
R if the answer is all real numbers. Type N if there is no solution.)
I’ll be using the ^ symbol for exponents.
11. Factor completely. 80a 2  200ad  125d 2 = 5(4a+5d)(4a+5d)
7 z  35 z  5

The answer is _________. (Simplify your
10
55 z
answer. Use integers or fractions for any numbers in the expression.)
12. Divide and simplify.
77z
2
13. Perform the indicated operations and simplify.
y  4 y 1
y  15

 2
=_______.
y  5 y  5 y  25
6
y+5
14. Multiply. (b  t )(b 2  bt  t 2 ) = b^3+t^3 (Simplify your answer.)
15. Identify the degree of each term of the polynomial and the degree of the polynomial.
 8 x 3  3x 2  2 x  9 The degree of the first term is 3 The degree of the second term is
2 The degree of the third term is 1 The degree of the fourth term is 0 The degree of the
polynomial is 3
16. Add. Simplify if possible.
9s
s

= ________. (Simplify your answer.)
s 9 s 3
2
s^2+12s
s^2-9
17. Divide. (42b 3  23b 2  44b  54)  (6b  5)
7b^2-2b+9+9/(6b+5)
18. Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard for m, ax 2  bx  c  0 . Solution: 4, only solution. The
equation is x^2-8x+16 = 0
1
1
19. Multiply. ( a  )( a  ) = a^2+7/10 a + 1/10 (Simplify your answer.)
5
2
I’ll be using the ^ symbol for exponents.
20. If a pro basketball player has a vertical leap of about 20 inches, what is his hang time?
Use the hang-time function V  48T 2 . His hang-time is 0.6 seconds. (Simplify your
answer. Type an integer or decimal. Round to the nearest tenth.)
21. Solve. s 2  6 s  27  0 . The solution is s = -9, 3 (Use a comma to separate answers
as needed. Type N if there is no solution.)
4y2
4y  4
= _______. (Type exponential notation

2
2y
4y  8y  4
with positive exponents.)
22. Multiply and simplify
2y
y-1
23. Rationalize the denominator. Assume that all expressions under radicals represent
r  s  2 rs
r s
positive numbers.
=
(Simplify your answer. Type an exact
rs
r s
answer, using radicals as needed.)
24. Subtract. Simplify, if possible.
3  w 4w  5

= _________. (Simplify your
w8 8 w
answer.)
3w-2
w-8
25. If the sides of a square are lengthened by 8 cm, the area becomes 144 cm 2 . Find a
length of a side of the original square. The length of a side of the original square is 6
cm.
26. Multiply and simplify. Assume variables represent nonzero real numbers. c16  c 0 =
c 16 (Simplify your answer. Type exponential notation with positive exponents.)
27. Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 3 hours.
How much time would it take for them to mow the lawn together? They could mow the
lawn in 1 5/7 hours if they worked together.
28. Simplify by factoring. Assume that all expressions under radicals represent
nonnegative numbers.
needed.)
12a 2 b = 2a 3b (Type an exact answer, using radicals as
I’ll be using the ^ symbol for exponents.
29. Add.
(4r 4  4r 3  4r 2  14r  7)  (r 5  10r 3  5r 2  4r  3)  (7r 4  r 2  6r  5)
The answer is r^5-3r^4+6r^3+10r^2+4r-9 (Simplify your answer.)
30. Rewrite the following expression with positive exponents. (24 xy)
1
(24xy)^9/10

9
10
1
= -1/2 (Simplify your answer. Type a fraction or integer. Type N if
8
the root is not a real number.)
31. Simplify.
3

32. Solve. v 2  6v  27  0 The solution is: v = -3, 9 (Use a comma to separate
answers. Type N if there is no solution.)
33. Use the quadratic formula to solve the equation. 2 x 2  3x  6 The solution set is
{_____}. (Simplify your answer. Type an exact answer, using radicals as needed.
Express complex numbers in terms of i and use integers or fractions for any numbers
in the expression. Use a comma to separate answers as needed.)
3  i 39 3  i 39
,
4
4
34. Factor completely. 5c 2  81  90c  _______. (Type N if the expression is not
factorable.)
I think you made a typo… I bet it’s 25c^2, not 5.
If so:
(5c-9)(5c-9)
35. Television sets. What does it mean to refer to a 20-in. TV set or a 25-in. TV set? Such
units refer to the diagonal of the screen. A 20 in. TV set also has a width of 16 inches.
The height of a 20-in. TV is 12 inches.
36. Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers.
in radical form.)
37. Find the following.
real number.)
12
3
y 10 3 81y 11 = 3y 7
3
3 (Simplify your answer. Type
(2)12 = 2 (Simplify your answer. Type N if the root is not a
I’ll be using the ^ symbol for exponents.
39. Multiply. (3 3  6 5 )(5 3  10 5 ) = -255 (Simplify your answer. Type an exact
answer, using radicals as needed.)
40. In a right triangle, find the length of the side not given. b = 1, c = 26 The length
of the third side is 5 (Simplify your answer. Type an exact answer, using radicals as
needed.)
3x 2  5 x  6
41. Evaluate the polynomial for x = 2.
When x = 2, 3 x 2  5 x  6 = 8 (Simplify your answer.)
42. Factor out the greatest common factor. 5 x 5  40 x 4  15 x 3 .
The factorization is 5x^3(x^2-8x+3) (Type your answer in factored form.)
1
1
1
43. Use rational exponents to write x 4  y 2  z 3 as a single radical expression.
12throot(x^3y^6z^4)
44. Factor completely. 49v 2  9 = (7v-3)(7v+3) (Type N if the binomial is not
factorable.)
45. Solve. x 2  6 x  4  0 The solution is x = __________. (Simplify your answer. Use
a comma to separate answers. Type exact answers, using radicals as needed. Type N if
there is no solution.)
-3+sqrt 13, -3-sqrt 13
46. Simplify by removing factors of 1.
7m 2  7m
The simplified form is __________.
42m 2  49m
m+1
6m+7
47. Factor. c 2  18c  81 = (c+9)(c+9)
(Type N if the trinomial is not factorable.)
48. Find the following. Assume that variables can represent any real number.
|a+9|
( a  9) 2 =
I’ll be using the ^ symbol for exponents.
49. Solve. 9 x  55  x  5 The solution is x = 5 (Use a comma to separate answers.
Type N if the solution is not a real number.)
50. Factor. 15  8s  s 2 = (s-5)(s-3)
(Type N if the trinomial is not factorable.)
51. Find the greatest common factor for the group of terms  66a 2 ,11a 5 The greatest
common factor is 11a^2
52. Find the vertex, line of symmetry, the maximum or minimum value of the quadratic
function, and graph the function. f ( x)  2 x 2  2 x  7
The x-coordinate of the vertex is 1/2 (Type a simplified fraction.)
The y-coordinate of the vertex is 15/2 (Type a simplified fraction.)
The equation of the line of symmetry is x = 1/2 (Type a simplified fraction.)
The max/min of f(x) is 15/2 (Type a simplified fraction.)
1 15
The value, f ( ) 
is? Maximum
2
2
53. Add. (5 x 2  6 xy  y 2 )  (8 x 2  2 xy  y 2 )  ( x 2  xy  2 y 2 ) The answer is
-2x^2-7xy-2y^2
54. A) Solve. 5 x 2  15 What are the solutions? x = __________. (Type an exact
answer using radicals as needed. Rationalize all denominators. Express complex numbers
in terms of i and use a comma to separate answers as needed.)
B) Find the intercepts of f ( x)  5x 2  15 What are the x-intercepts? _________.
(Type an ordered pair. Type an exact answer, using radicals as needed. Rationalize all
denominators. Express complex numbers in terms of i and use commas to separate
answers as needed. Type N if there are no x-intercepts.)
sol: sqrt 3, -sqrt 3
Inter: (sqrt 3, 0), (-sqrt 3, 0)
I’ll be using the ^ symbol for exponents.
55. Factor the trinomial. r 3  5r 2  36r The answer is r(r-9)(r+4) (Type N if the
trinomial is not factorable.)
56. Use the FOIL method to find the product. (5 x 6  8)( x 9  8) = 5x^15-8x^9-40x^6+64
57. For the following equation, state the value of the discriminate and then describe the
nature of the solutions.  5 x 2  4 x  2  0
The value of the discriminate is -24
The equation has two imaginary solutions
58. Multiply. (3z ) 2 (2 z 9 ) 3 = 72z^29
59. Find a polynomial for the perimeter and for the area. Of four sides, side a = x  10
And side b = x.
The perimeter is 4x+20 (Simplify you answer. Do not factor.)
The area is x^2+10x Simplify you answer. Do not factor.)
s3  7x
s 2  49
The numbers for which the rational expression in undefined are -7, 7 (Use a comma to
separate answers.)
60. Find all numbers for which the rational expression in undefined.
61. Convert to decimal notation. 8.54  10 7 = 85400000 (Simplify your answer. Type an
integer to decimal.)
62. Find the variation constant and an equation of variation where y varies directly as x
and y = 12 when x = 4.
The variation constant is 3
The equation of variation is y = 3x
63. Find the vertex, line of symmetry, the maximum or minimum value of f(x). Graph the
function.
You didn’t post the equation… but based on the question I can help with a couple parts.
The vertex is (-4, 4) (Type an ordered pair.)
The line of symmetry is x = -4
What is the max/min value of f(x)? 4
Is the value f(-4) = 4 a minimum or maximum? __________.
64. Rewrite with a rational exponent.
6
21 = 211/6 (Simplify your answer.)
65. Solve for x. 4 x( x  2)  5 x( x  1)  2 x = -2, -1 ((Simplify your answers. Use a
comma to separate answers. Type N if there is no solution.)
I’ll be using the ^ symbol for exponents.
66. Simplify by taking roots of the numerator and the denominator. Assume that all
4x 4 3 x 2
64 x 14
=
(Type an
y
y3
exact answer, using radicals as needed. Type N if the root is not a real number.)
expressions under radicals represent positive numbers.
3