Free Printable Final Review #2

1.

Divide:
(9x² + 6x) ÷ 3x

a)

3x + 2

b)

3x² + 2x

c)

5x²

d)

3x + 6

2.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

3.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

4.

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

a)

x⁴

b)

x³

c)

x²

d)

x

5.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

6.

Which would be better to use here?

a)

Long division

b)

Synthetic division

7.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

8.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

9.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

10.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

11.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

12.

2x³ - 5x² + 3x + 7 ÷ x - 2

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

13.

3x³ + 5x - 1 ÷ x + 1

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

14.

Find the Quotient
(2x³ - 5x² - 3x + 7) / (x - 2)

a)

2x²- 9x +15

b)

2x² - x - 5

c)

2x² - 9x - 21

d)

2x² + x + 5

15.

Classify:
2x⁴+14x³−2x²

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

16.

Classify:
2n³

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

17.

Classify:
x³ + 3x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

18.

What is the name for this polynomial? 2x² + 3x - 1

a)

Quadratic Trinomial

b)

Linear Binomial

c)

Quartic Trinomial

d)

Quintic Trinomial

19.

What is the name for this polynomial? 3z

a)

Constant Monomial

b)

Linear Binomial

c)

Linear Monomial

d)

Bionic Monomial

20.

What is the name of this polynomial? 4x³ - 2x² + 7x - 3

a)

Septic Polynomial with Four Terms

b)

Quadratic Polynomial with Four Terms

c)

Quintic Polynomial with Four Terms

d)

Cubic Polynomial with Four Terms

21.

What is the name of this polynomial? 3x⁵ + 2

a)

Quintic Binomial

b)

5th Degree Monomial

c)

5th Degree Trinomial

d)

Quintic Polynomial with Four Terms

22.

What is the name of this polynomial? 3

a)

Constant Monomial

b)

Linear Monomial

c)

Quartic Monomial

d)

Cubic Monomial

23.

If a polynomial is a constant, its degree is...

a)

1

b)

0

c)

-1

d)

98

24.

What is the degree of this polynomial: 5x⁶ + 3x² - 8x¹⁰

a)

2

b)

10

c)

6

d)

8

25.

How many terms are in a binomial?

a)

0

b)

1

c)

2

d)

4

26.

If a polynomial is considered linear, its degree is...

a)

2

b)

3

c)

1

d)

98

27.

Once simplified, how many terms are in the expression:

a)

2

b)

3

c)

4

d)

5

e)

6

28.

What are terms that have the same variable and exponent called?

a)

Coefficients

b)

Like Terms

c)

Constants

d)

Monomials

29.

What is the degree of this polynomial: 5x⁶ + 3x² - 8x¹⁰

a)

2

b)

10

c)

6

d)

8

30.

Re-write using a rational exponent: $\sqrt{x}$

a)

$x^{\frac{1}{2}}$

b)

$\frac{x}{2}$

c)

$\frac{1}{2}x$

d)

$x^2$

31.

Re-write using rational exponents:

a)

$a^{\frac{3}{2}}$

b)

$a^{\frac{2}{3}}$

c)

$a^{1.5}$

d)

$\frac{a^2}{3}$

e)

$\frac{1}{a^{\frac{2}{3}}}$

32.

Simplify the expression:
27^1/3

a)

3

b)

9

c)

27

d)

3³

33.

Simplify the expression:
36^1/2

a)

6

b)

36

c)

-6

d)

1296

34.

Simplify:

a)

2

b)

8

c)

16

d)

32

35.

Simplify:

a)

2

b)

4

c)

16

d)

64

36.

64^4/3

a)

256

b)

8

c)

8⁴

d)

2

37.

125^2/3

a)

5

b)

25

c)

75

d)

5

38.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

39.

When simplifying a value with a rational exponent, which part should you do first?

a)

Root

b)

Power

40.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

41.

Write the expression in exponential form:
√23

a)

23^1/2

b)

23^-1/2

c)

23²

d)

23^-2

42.

Write the expression in exponential form:
∛x²

a)

x^3/2

b)

x^2/3

c)

x^1/2

d)

x^1/3

43.

Write the expression in radical form.
y^1/2

a)

√y

b)

∛y

c)

√y²

d)

∛y²

44.

Write the expression in radical form.
x^1.5

a)

√x³

b)

∛x²

c)

x³

d)

√x

45.

Write the expression in radical form.
x^7/2

a)

√x⁷

b)

7√x²

c)

7x²

d)

∛x⁷

46.

True or False:

a)

True

b)

False

47.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

48.

Simplify
m⁵⋅m²

a)

m⁷

b)

m³

c)

m¹⁰

d)

m²

49.

Simplify
(y³)⁵

a)

y¹⁵

b)

y⁸

c)

y⁻²

d)

y

50.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

51.

Simplify: $6^5\cdot6^2$

a)

$6^7$

b)

$6^3$

c)

$36^7$

d)

$6^{10}$

52.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

53.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

54.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

55.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

56.

Simplify: $\left(4y\right)^{-3}$

a)

$\frac{1}{64y^3}$

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

$\frac{64}{y^3}$

57.

Simplify: $\left(2m\right)^5$

a)

$10m^5$

b)

$32m^5$

c)

$25m^5$

d)

$\frac{1}{2m^5}$

58.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

59.

Simplify: $\left(3k^5\right)\left(-2k^3\right)$

a)

$6k^8$

b)

$-6k^{15}$

c)

$6k^{15}$

d)

$-6k^8$

60.

Simplify: $\left(\frac{4}{2d^2}\right)^3$

a)

$\frac{2}{d^2}$

b)

$\frac{8}{d^6}$

c)

$\frac{8}{2d^2}$

d)

$\frac{64}{2d^2}$

61.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

62.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

$\frac{y^3}{2x}$

c)

$\frac{4y^3}{8x}$

d)

$1$

63.

Evaluate ∛1

a)

1

b)

2

c)

3

d)

4

64.

∛125

a)

5

b)

4

c)

6

d)

7

65.

$\frac{∛8}{∛27}=$

a)

$\frac{2}{3}$

b)

$\frac{3}{2}$

c)

$\frac{-2}{3}$

d)

$\frac{-3}{2}$

66.

∛-1

a)

1

b)

-1

c)

i

d)

-i

67.

∛1331

a)

21

b)

9

c)

8

d)

11

68.

∛343

a)

10

b)

9

c)

8

d)

7

69.

a)

A

b)

B

c)

C

d)

D

70.

a)

A

b)

B

c)

C

d)

D

71.

a)

A

b)

B

c)

C

d)

D

72.

a)

A

b)

B

c)

C

d)

D

73.

a)

A

b)

B

c)

C

d)

D

Final Review #2

Total questions: 73

Worksheet time: 3hrs 36mins

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