Master Polynomial Functions: Online Quizzes and Practice Tests

Question 1

Which of the following is a polynomial expression of degree 3?

Accepted Answer

x^3 - 2x^2 + x + 5

Answer

x + y + z

Answer

x^2 + 2x - 3

Answer

sqrt(x) + x^2

Question 2

What is the end behavior of the polynomial function: f(x) = -x^4 + 2x^2 + 1?

Accepted Answer

As x approaches infinity, f(x) approaches -infinity.

Answer

As x approaches infinity, f(x) approaches 1.

Answer

As x approaches negative infinity, f(x) approaches infinity.

Answer

As x approaches negative infinity, f(x) approaches 1.

Question 3

Which of the following is an example of a real-world application of polynomial functions?

Accepted Answer

Modeling the trajectory of a projectile

Answer

Calculating the area of a circle

Answer

Finding the volume of a cone

Answer

Solving a quadratic equation

Question 4

What is the leading coefficient of the polynomial function: f(x) = -2x^3 + x^2 - 5?

Accepted Answer

-2

Answer

1

Answer

-5

Answer

0

Question 5

Simplify the following rational expression: (x² - 9) / (x + 3)

Accepted Answer

x - 3

Answer

x + 3

Answer

(x + 3) / (x - 3)

Answer

(x - 3) / (x + 3)

Question 6

Which graph represents the polynomial function: f(x) = x³ - 2x² + x - 2?

Accepted Answer

Cubic function with a local minimum and maximum

Answer

Parabola opening upward

Answer

Parabola opening downward

Answer

Line with a positive slope

Question 7

What is the leading coefficient of the polynomial -2x³ + 5x² - 3x + 1?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-3

Question 8

Which expression represents a second-degree polynomial?

Accepted Answer

x^2 + 3x - 2

Answer

2x - 5

Answer

sin(x) + cos(x)

Answer

e^(-x) + 1

Question 9

Simplify the rational expression (x² - 9) / (x + 3):

Accepted Answer

x - 3

Answer

x + 3

Answer

(x - 3)(x + 3)

Answer

(x + 3)²

Question 10

Identify the leading coefficient of the polynomial -2x⁵ + 3x² - x + 7:

Accepted Answer

-2

Answer

3

Answer

-1

Answer

7

Question 11

Determine the multiplicity of the zero x = 2 in the polynomial x³ - 4x² + 4x - 16:

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 12

Which of the following is NOT a characteristic of polynomial functions?

Accepted Answer

Asymptotic

Answer

Continuous

Answer

Smooth

Answer

Infinitely differentiable

Question 13

Factor the polynomial completely: x^3 - 8

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)^3

Answer

(x + 2)^3

Question 14

What is the leading coefficient of the polynomial: -3x^5 + 2x^3 - x + 7?

Accepted Answer

-3

Answer

2

Answer

-1

Answer

7

Question 15

Which of the following transformations will shift the graph of y = x^2 up by 3 units?

Accepted Answer

y = x^2 + 3

Answer

y = (x + 3)^2

Answer

y = x^2 - 3

Answer

y = (x - 3)^2

Question 16

What is the degree of the polynomial f(x) = 3x^4 - 2x^2 + 5?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 17

Factor the polynomial f(x) = x^2 - 4.

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(2x - 1)^2

Answer

The polynomial is not factorable over real numbers

Question 18

Simplify the rational expression (x^2 - 4) / (x + 2).

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 - 2x + 4

Answer

The expression cannot be simplified

Question 19

What is the leading coefficient of the polynomial f(x) = -3x^4 + 2x^3 - 5x + 1?

Accepted Answer

-3

Answer

2

Answer

-5

Answer

1

Question 20

Which of the following polynomials has a positive leading coefficient and an even degree?

Accepted Answer

f(x) = -x^6 + 4x^4 - 5x^2 + 6

Answer

f(x) = x^3 - 2x^2 + x - 1

Answer

f(x) = -x^4 + 2x^2 - 3x + 5

Answer

f(x) = x^5 - 3x^3 + 2x - 1

Question 21

Find the domain of the polynomial function f(x) = sqrt(x - 2).

Accepted Answer

x ≥ 2

Answer

x < 2

Answer

x > 2

Answer

All real numbers

Question 22

Which of the following is NOT a characteristic of polynomials?

Accepted Answer

Periodic

Answer

Continuous

Answer

Differentiable

Answer

Degree is a non-negative integer

Question 23

Simplify the rational expression: (x² - 1) / (x + 1)

Accepted Answer

x - 1

Answer

x + 1

Answer

x² - 1

Answer

(x - 1)²

Question 24

Find the zeros of the polynomial function: f(x) = x² - 4x + 3

Accepted Answer

x = 1, x = 3

Answer

x = -1, x = -3

Answer

x = 2, x = 1.5

Answer

x = -2, x = -1.5

Question 25

Identify the leading coefficient of the polynomial g(x) = -3x³ + 2x² - 5x + 1:

Accepted Answer

-3

Answer

-2

Answer

3

Answer

5

Question 26

Given that the polynomial h(x) has a zero at x = 2, identify a factor of h(x):

Accepted Answer

x - 2

Answer

x + 2

Answer

(x - 2)²

Answer

(x + 2)²

Question 27

Given the polynomial p(x) = x² + bx + c, where p(x) is divisible by x - 2 without a remainder, what is the value of c?

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 28

Identify the graph that corresponds to the polynomial function f(x) = -x³ + 3x² - 2x + 1:

Accepted Answer

A downward-facing parabola

Answer

An upward-facing parabola

Answer

A line with a positive slope

Answer

A line with a negative slope

Question 29

Given that x = 2 is a zero of the polynomial P(x), which of the following must be a factor of P(x)?

Accepted Answer

x - 2

Answer

x^2 - 2

Answer

x + 2

Answer

x^2 + 2

Question 30

Identify the degree of the polynomial function: f(x) = 2x^3 + 3x^2 - 4x + 1

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 31

Which of the following is NOT a root of the polynomial equation: x^4 - 16 = 0?

Accepted Answer

x = -1

Answer

x = 2

Answer

x = -2

Answer

x = 4

Question 32

Solve the polynomial equation: x³ - 4x² + 3x = 0

Accepted Answer

x = 0, 1, 3

Answer

x = 0, -1, 3

Answer

x = 0, 2, 3

Answer

x = 0, 1, -3

Question 33

Which of the following is a root of the polynomial equation x³ - 8 = 0?

Accepted Answer

x = -2

Answer

x = 2

Answer

x = 4

Answer

x = -4

Question 34

Factor the polynomial expression: x⁴ + 2x² - 3

Accepted Answer

(x² + 3)(x² - 1)

Answer

(x² - 3)(x² + 1)

Answer

(x² + 1)(x² - 3)

Answer

(x² - 1)(x² + 3)

Question 35

Find the degree of the polynomial function f(x) = 3x⁵ - 2x³ + 4x - 1

Accepted Answer

5

Answer

3

Answer

6

Answer

7

Question 36

Identify the polynomial function among the following:

Accepted Answer

y = x^3 - 2x^2 + x - 1

Answer

y = √x

Answer

y = e^x

Answer

y = sin(x)

Question 37

Factor the polynomial expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 4)(x - 4)

Answer

(x - 2)^2

Question 38

Find the degree of the polynomial function: y = 5x^(6) - 3x^(4) + 2x - 1

Accepted Answer

6

Answer

4

Answer

5

Answer

2

Question 39

Identify the leading coefficient of the polynomial: y = -2x^5 + 3x^3 - x + 7

Accepted Answer

-2

Answer

7

Answer

3

Answer

-1

Question 40

Which of the following expressions represents a polynomial function?

Accepted Answer

f(x) = 2x³ - 5x + 1

Answer

f(x) = x² - 1 / x + 2

Answer

f(x) = √x

Answer

f(x) = sin(x) + cos(x)

Question 41

What is the degree of the polynomial f(x) = 3x⁴ - 2x² + 5?

Accepted Answer

4

Answer

5

Answer

3

Answer

2

Question 42

Factor the polynomial expression: x² - 4x + 4

Accepted Answer

(x - 2)²

Answer

Cannot be factored

Answer

(x + 2)²

Answer

(x - 4)²

Question 43

Solve the polynomial equation: 2x³ - 5x² + 3x - 2 = 0

Accepted Answer

x = 1 or x = 2

Answer

x = 1 or x = -2

Answer

x = -1 or x = 2

Answer

x = -1 or x = -2

Question 44

The graph of the polynomial function f(x) = x³ - 2x² - x + 2 will have:

Accepted Answer

A local maximum and a local minimum

Answer

Only a local maximum

Answer

Only a local minimum

Answer

No local extrema

Question 45

What is the end behavior of the polynomial function f(x) = -3x⁴ + 2x³ - 5x + 1?

Accepted Answer

As x approaches positive infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Answer

As x approaches positive infinity, f(x) approaches positive infinity. As x approaches negative infinity, f(x) approaches negative infinity.

Question 46

The polynomial function f(x) = 2x⁵ - 3x³ + 4x - 1 has:

Accepted Answer

An odd degree and a negative leading coefficient.

Answer

An odd degree and a positive leading coefficient.

Answer

An even degree and a positive leading coefficient.

Question 47

Which of the following expressions represents a polynomial function?

Accepted Answer

f(x) = 3x² + 2x - 1

Answer

f(x) = e^x

Answer

f(x) = x^(1/2) + 5

Answer

f(x) = sin(x)

Question 48

What is the degree of the polynomial p(x) = 2x³ - 5x² + 7x - 1?

Accepted Answer

3

Answer

4

Answer

5

Answer

2

Question 49

Factor the polynomial expression: x² - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)²

Answer

(x - 4)(x + 4)

Question 50

Which of the following is the graph of the polynomial function f(x) = x^2 - 4?

Accepted Answer

A parabola opening upwards

Answer

A straight line

Answer

A parabola opening downwards

Answer

A circle