Polynomials: Expressions with Variables and Constants - Interactive Learning Quiz

Question 1

Which of the following expressions is a polynomial?

Accepted Answer

x^2 + 2x - 3

Answer

x^2 / (2x + 1)

Answer

√x + 1

Answer

2^x + 3

Question 2

Which of the following is a degree 3 polynomial?

Accepted Answer

x^3 - 2x^2 + 5x - 1

Answer

x^2 + 2x - 3

Answer

2x^4 + 3x^2 - x + 5

Answer

√x + 2

Question 3

Expand the binomial: (x + 2)^3

Accepted Answer

x^3 + 12x^2 + 24x + 16

Answer

x^3 + 6x^2 + 12x + 8

Answer

x^3 + 8

Answer

x^3 + 3x^2 + 3x + 1

Question 4

Which of the following is a characteristic of a polynomial function?

Accepted Answer

It is a continuous function

Answer

It has a turning point at x = 0

Answer

It is always increasing

Answer

It is always decreasing

Question 5

Find the degree of the polynomial 3x^4 - 2x^2 + 1:

Accepted Answer

4

Answer

1

Answer

2

Answer

6

Question 6

Simplify the polynomial (2x + 3) - (x - 5):

Accepted Answer

x + 8

Answer

x - 2

Answer

3x + 8

Answer

x + 2

Question 7

Factor the polynomial x^2 - 4:

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x + 4)(x - 4)

Answer

Cannot be factored

Question 8

Which of the following expressions is a rational expression?

Accepted Answer

(x + 2) / (x - 3)

Answer

x + 1

Answer

x^2 - 1

Answer

e^x

Question 9

What is the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0

Answer

a + bx + c = 0

Answer

ax + b = c

Answer

ax^2 + c = 0

Question 10

What is the degree of the polynomial: 2x³ + 5x² - 7x + 1?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 11

Factor the following polynomial:
(x^2 - 4)
(A) (x - 2)(x + 2)
(B) (x - 4)(x + 4)
(C) (x - 2)(x - 2)
(D) (x + 4)(x + 4)

Accepted Answer

(A)

Answer

(B)

Answer

(C)

Answer

(D)

Question 12

Simplify the polynomial: (x^2 + 2x - 3) + (2x^2 - x + 4)

Accepted Answer

3x^2 + x + 1

Answer

3x^2 - x + 1

Answer

3x^2 + 3x + 1

Answer

3x^2 - 3x + 1

Question 13

What is the leading coefficient of the polynomial: 4x^3 - 2x^2 + 5x - 1?

Accepted Answer

4

Answer

2

Answer

5

Answer

-1

Question 14

Determine the degree of the polynomial: 2x^4 - 3x^3 + 4x^2 - 5x + 1

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 15

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)(x^2 + 4)

Answer

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

Question 16

Which of the following is a polynomial?

Accepted Answer

x^2 - 5x + 6

Answer

2x + 3y

Answer

e^(2x)

Answer

sin(x)

Question 17

Find the degree of the polynomial 3x^4 - 2x^3 + x - 5.

Accepted Answer

4

Answer

1

Answer

3

Answer

5

Question 18

Which of the following is a quadratic polynomial?

Accepted Answer

x^2 + 3x - 4

Answer

x + 2

Answer

x^3 - 2x + 1

Answer

e^x

Question 19

Which of the following is not a valid polynomial?

Accepted Answer

√x + 3

Answer

x³ + 2x² - 5x

Answer

2x⁴ - x² + 1

Answer

(x - 1)(x + 2)

Question 20

Factor the polynomial x² - 9:

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)²

Answer

(x + 3)²

Question 21

Identify the leading coefficient of the polynomial -3x⁴ + 2x³ - 5x² + 1:

Accepted Answer

-3

Answer

2

Answer

-5

Answer

1

Question 22

Factor the polynomial x³ + 8:

Accepted Answer

(x + 2)(x² - 2x + 4)

Answer

(x - 2)(x² + 2x + 4)

Answer

(x + 2)³

Answer

(x - 2)³

Question 23

Factor the polynomial: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)(x - 2)

Answer

(x + 2)(x + 2)

Answer

(x - 2)(x + 2)

Question 24

What is the degree of the polynomial: (x^2 + 1)(x - 3)?

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 25

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

Accepted Answer

x + 2

Answer

x - 2

Answer

(x + 2)(x - 2)

Answer

(x - 2)(x + 2)

Question 26

Which of the following expressions represents a polynomial?

Accepted Answer

x^3 + 2x^2 - 5

Answer

√x + 3

Answer

2sin(x) + 1

Answer

x^-2

Question 27

Determine the degree of the polynomial: 5x^4 - 2x^3 + 7

Accepted Answer

4

Answer

7

Answer

Cannot be determined

Answer

3

Question 28

Which of the following is an example of a monomial?

Accepted Answer

5x^2

Answer

x^2 - 3x + 2

Answer

x + 2

Question 29

Identify the polynomial function:

Accepted Answer

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

Answer

f(x) = √x + 1

Answer

f(x) = sin(x)

Answer

f(x) = |x|

Question 30

Determine the remainder when f(x) = x^3 - 2x^2 + x - 3 is divided by (x - 1)

Accepted Answer

-1

Answer

1

Answer

-2

Answer

2

Question 31

Which of these expressions is a polynomial?

Accepted Answer

x² + 3x - 5

Answer

√x + 2

Answer

sin(x) + cos(x)

Question 32

Factor the polynomial: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)²

Answer

(x² + 9)(x - 1)

Answer

(x + 9)(x - 1)

Question 33

Solve the polynomial equation: x² - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = 1, x = 6

Answer

x = -2, x = -3

Question 34

What is the degree of the polynomial: 4x³ - 2x² + 3x - 1?

Accepted Answer

3

Answer

4

Answer

2

Question 35

What is the leading coefficient of the polynomial: -x⁴ + 2x³ - 3x² + 4?

Accepted Answer

-1

Answer

1

Answer

-4

Answer

2

Question 36

What is the end behavior of the polynomial: f(x) = -2x⁵ + 3x³ - x²?

Accepted Answer

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

Answer

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

Answer

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

Question 37

What is the constant term of the polynomial: 2x⁴ - 3x³ + 4x - 5?

Accepted Answer

-5

Answer

2

Answer

0

Answer

4

Question 38

How many zeros does the polynomial f(x) = x³ - 2x² + x - 2 have?

Accepted Answer

3

Answer

2

Answer

1

Answer

4

Question 39

What is the remainder when the polynomial f(x) = x³ - 2x² + 3x - 4 is divided by (x - 1)?

Accepted Answer

-1

Answer

0

Answer

2

Answer

1

Question 40

What is the degree of the polynomial 7x³ - 4x² + 9?

Accepted Answer

3

Answer

2

Answer

9

Answer

7

Question 41

Simplify the polynomial expression: (3x² + 2x - 5) + (x² - 7x + 1)

Accepted Answer

4x² - 5x - 4

Answer

2x² - 5x - 4

Answer

4x² + 9x - 6

Question 42

Multiply the polynomials: (2x - 3)(x + 4)

Accepted Answer

2x² + 5x - 12

Answer

2x² - x - 12

Answer

2x² - 12

Question 43

Factor the quadratic expression: x² + 7x + 12

Accepted Answer

(x + 3)(x + 4)

Answer

(x + 6)(x + 2)

Answer

(x + 1)(x + 12)

Question 44

Which of the following is NOT a polynomial?

Accepted Answer

√x + 2

Answer

x² - 3x + 5

Answer

8

Answer

2x⁴ - x³/2 + 7

Question 45

What is the leading coefficient of the polynomial -5x⁴ + 2x³ + 7x - 9?

Accepted Answer

-5

Answer

-9

Answer

4

Answer

2

Question 46

If (x - 3) is a factor of a polynomial P(x), what is the value of P(3)?

Accepted Answer

0

Answer

Cannot be determined

Answer

-3

Answer

3

Question 47

The area of a rectangle is represented by the polynomial 2x² + 9x + 10. If its width is (x + 2), what is its length?

Accepted Answer

2x + 5

Answer

x + 10

Answer

x + 5

Answer

2x + 10

Question 48

Solve the quadratic equation: x² - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = -1, x = -6

Answer

x = 1, x = 6

Answer

x = -2, x = -3

Question 49

Which of the following is NOT a polynomial?

Accepted Answer

√x + 1

Answer

3x² + 2x - 5

Answer

x³ + 2x² + 5x

Answer

4x⁴ - 7

Question 50

Factor the polynomial x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x + 9)(x + 1)

Answer

(x - 9)(x - 1)

Question 51

What is the sum of the polynomials 3x² + 2x - 1 and 2x² - 5x + 4?

Accepted Answer

5x² - 3x + 3

Answer

5x² + 3x + 3

Answer

x² - 3x + 3