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11/4/2016
Practice problems for Exam 3 (not for credit)­Luiza DeSouza
Instructor: Luiza DeSouza
Course: MATH 0110­ Intermediate
Algebra­ Fall 2016
Student: Luiza DeSouza
Date: 11/4/16
Assignment: Practice problems for
Exam 3 (not for credit)
1. Evaluate the expression. Assume that all bases are not equal to 0.
0
5z + 6
0
5z + 6 =
(Simplify your answer.)
2. Simplify. Use positive exponents for any variables.
− 10 5
4z
z
−5
z
− 10 5
4z
z
=
−5
z
3. Simplify. Use positive exponents for any variables.
2
−1
−1
+5
−2
−2
2
+5
=
(Type an integer or a simplified fraction.)
4. Simplify. Use positive exponents for any variables.
−6
6x
yz
−3
4
3x yz
6x
−6
yz
−3
=
4
3x yz
(Simplify your answer. Type exponential notation with positive exponents.)
5. Simplify.
2x
y
2x
y
5
5
2
−2
2
=
−2
(Use positive exponents only.)
6. Simplify. Write each answer using positive exponents only.
3
(4a bc
3
(4a bc
−4 −3
−4 −3
)
)
=
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
7. Simplify. −4
4 −1
x y
−2
z
−4
4 −1
x y
z
=
−2
(Use positive exponents only.)
8. Simplify.
−3
−4 2
5a
b
4 6
10a b
5a
−3
−4 2
b
=
4 6
10a b
(Type exponential notation with positive exponents. Use integers or fractions for any numbers in the expression.)
9. Simplify. Write the answer using positive exponents only.
8
(3x y)
8
−1
(3x y)
−1
7 6
(7x y ) 7 6
(7x y ) =
10. Simplify. 2
2
x (x bc)
2
2
x (x bc)
−3
−3
=
(Use positive exponents only.)
11. Simplify.
4x
y
4x
y
2
3
2
4x
3
3
6
−2
y
4x
3
y
6
−2
=
(Simplify your answer. Use positive exponents only.)
12. Simplify the following. Assume that variables in the exponents represent integers and that all other variables are not 0.
(x
(x
4a + 3 6
)
4a + 3 6
) =
(Simplify your answer.)
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
13. Simplify the following. Assume that variables in the exponents represent integers and that all other variables are not 0.
x
5a
x
x
5a
x
(x
(x
5a 5
)
5a − 2
5a 5
)
=
5a − 2
(Simplify your answer.)
14. Simplify the expression.
4(z − 6) − 3(3z + 1)
4(z − 6) − 3(3z + 1) =
(Simplify your answer.)
15. Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these.
2
2
x y − 3xy + 3x + y
5
The degree of the polynomial is 2
2
.
5
Is x y − 3xy + 3x + y a monomial, binomial, trinomial, or none of these?
A. Monomial
B. Binomial
C. Trinomial D. None of these
16. Perform the indicated operation.
2
2
Subtract ( − x + 3x ) from (3x − 12x ).
The difference between the two polynomials is (Simplify your answer. Do not factor.)
. 17. Perform the indicated operation.
3
2
3
2
( − 8x − 6x − 8x − 12 ) − ( − 5x − 3x − 9x + 12 )
3
2
3
2
( − 8x − 6x − 8x − 12 ) − ( − 5x − 3x − 9x + 12 ) =
(Simplify your answer. Do not factor.)
18. Perform the indicated operations and simplify.
2
2
2
(7x − 4) + ( − 2x − 3) − (5x − 7)
2
2
2
(7x − 4) + ( − 2x − 3) − (5x − 7) =
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
19. For the following polynomial, find P(a), P( − x ) and P(x + h).
P(x) = 9x − 7
P(a) =
(Simplify your answer. Do not factor.)
P( − x ) =
(Simplify your answer. Do not factor.)
P(x + h) =
(Simplify your answer. Do not factor.)
20. Multiply. (s − 4)(2s + 6)
(s − 4)(2s + 6) =
(Simplify your answer.) 21. Multiply.
3
(3x + 5)(x − x + 2)
3
(3x + 5)(x − x + 2) =
(Simplify your answer.)
22. Multiply. (x + 1 )2
(x + 1 )2 =
(Simplify your answer.) 23. Multiply using special product methods.
2
(5x − y)
2
(5x − y) =
(Simplify your answer.)
24. Multiply.
2
(x − 10)(x + 10)(x + 100)
2
(x − 10)(x + 10)(x + 100) =
(Simplify your answer.)
25. If f(x) = x 2 − 5x + 3 , find
a. f(a + h)
b. f(a)
c. f(a + h) − f(a)
a. f(a + h) = b. f(a) = c. f(a + h) − f(a) = (Simplify your answer.) (Simplify your answer.)
(Simplify your answer.)
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
26. Find the greatest common factor (GCF) of 3
2 2
The GCF is 3
.
30a b , 24a b , and 54ab .
27. Factor out the greatest common factor from the following polynomial.
7
6
5x − 40x + 20x
5
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 5x 7 − 40x 6 + 20x 5 =
(Type your answer in factored form.)
B. The polynomial has no common factor other than 1.
28. Factor out the greatest common factor from the following polynomial.
7(x + 6) + a(x + 6)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 7(x + 6) + a(x + 6) =
(Type your answer in factored form.)
B. The polynomial has no common factor other than 1.
29. Factor the following polynomial by grouping.
ab + 5a + 3b + 15
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. ab + 5a + 3b + 15 = B. The polynomial has no common factor other than 1.
30. Factor the following polynomial by grouping.
ac + 7a − 2c − 14
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. ac + 7a − 2c − 14 =
B. The polynomial has no common factor other than 1.
31. Factor the following polynomial.
3
2
x − x − 15x + 15
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. x 3 − x 2 − 15x + 15 =
(Factor completely.)
B. The polynomial has no common factor other than 1.
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
32. Factor the following trinomial.
2
x + 5x + 4
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. x 2 + 5x + 4 =
(Type your answer in factored form.)
B. The polynomial is prime.
33. Factor the trinomial, or state that the trinomial is prime. Check the factorization using FOIL multiplication.
2
y − 5y + 6
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. y 2 − 5y + 6 =
B. The polynomial is prime.
34. Factor the trinomial completely.
2
x + 3x − 4
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. x 2 + 3x − 4 =
B. The polynomial is prime.
35. Factor the following trinomial.
2
x − 5x − 50
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. x 2 − 5x − 50 =
(Type your answer in factored form.)
B. The polynomial is prime.
36. Factor the trinomial.
2
3x z + 33xz + 84z
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 3x 2 z + 33xz + 84z =
(Factor completely.)
B. 3x 2 z + 33xz + 84z is prime.
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
37. Factor completely.
2
36x − 36x − 16
Select the correct choice below and fill in any answer box within your choice.
A. 36x 2 − 36x − 16 =
B. 36x 2 − 36x − 16 is prime.
38. Factor the trinomial completely.
2
6x − xy − 1y
2
Select the correct choice below and fill in any answer box within your choice.
A. 6x 2 − xy − 1y 2 =
B. 6x 2 − xy − 1y 2 is prime.
39. Use substitution to factor the polynomial completely.
4
2
x +x −6
Select the correct choice below and, if necessary, fill in any answer box within your choice.
A. x 4 + x 2 − 6 =
B. x 4 + x 2 − 6 is prime.
40. Use substitution to factor the polynomial completely.
2
(9x + 1) + 13(9x + 1) + 30
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
2
(9x + 1) + 13(9x + 1) + 30 =
(Simplify your answer. Factor completely.)
B. (9x + 1)2 + 13(9x + 1) + 30 is prime.
41. Use substitution to factor the polynomial completely.
2
(a − 7) − 3(a − 7) − 28
Select the correct choice below and fill in any answer box within your choice.
A. (a − 7)2 − 3(a − 7) − 28 =
(Simplify your answer.)
B. (a − 7)2 − 3(a − 7) − 28 is prime.
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
42. Factor the following trinomial completely.
2
25a − 10a + 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 25a2 − 10a + 1 =
B. 25a2 − 10a + 1 is prime.
43. Factor the following.
2 2
2
9y x + 30yx + 25x
2
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 9y 2 x 2 + 30yx 2 + 25x 2 =
B. 9y 2 x 2 + 30yx 2 + 25x 2 is prime.
44. Factor.
2
r − 36
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. r2 − 36 =
B. r2 − 36 is prime.
45. Factor the following.
2
(y − 2) − 64
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (y − 2)2 − 64 =
(Simplify your answer. Factor completely.)
B. (y − 2)2 − 64 is prime.
46. Factor.
s 3 + 27
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. s 3 + 27 =
B. s 3 + 27 is prime.
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
47. Factor.
3
s − 125
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. s 3 − 125 =
B. s 3 − 125 is prime.
48. Factor.
16v 2 − 81
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 16v 2 − 81 =
B. 16v 2 − 81 is prime.
49. Solve the equation.
(y + 8)(y + 5) = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {
}.
(Use a comma to separate answers as needed.)
B. The solution set is ∅.
50. Solve the equation. c 2 + 7c + 10 = 0
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution set is {
}.
(Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.)
B. The solution set is ∅.
51. Solve the following equation.
2
z + 30 = 13z
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {
}.
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is ∅.
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Practice problems for Exam 3 (not for credit)­Luiza DeSouza
52. Solve the equation.
x(5x + 6 ) = 8
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {
}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. The solution set is ∅.
53. Solve the equation.
3
y = 4y
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution set is {
}.
(Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.)
B. The solution set is ∅.
54. Solve the following equation.
2
x − 3x − 28 = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {
}.
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is ∅.
55. Solve the following equation.
3
3x = 12x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {
}.
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is ∅.
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