Polynomials: Master the Basics with Interactive Quizzes

Question 1

Calculate the product of (x + 4) and (x^2 - 2x + 3).

Accepted Answer

x^3 + 2x^2 - 5x + 12

Answer

x^3 - 2x^2 - 5x + 12

Answer

x^3 + 6x^2 - 5x + 12

Answer

x^3 - 6x^2 - 5x + 12

Question 2

Simplify: (x + y)^2 - (x - y)^2

Accepted Answer

4xy

Answer

2xy

Answer

x^2 + y^2

Answer

x^2 - y^2

Question 3

Factor the polynomial: x^3 - 8

Accepted Answer

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

Answer

(x - 2)^3

Answer

(x + 2)^3

Answer

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

Question 4

Combine like terms in the expression 2x^2 + 3x - x^2 + 5x.

Accepted Answer

3x^2 + 8x

Answer

x^2 + 8x

Answer

3x^2 + 2x

Answer

x^2 + 2x

Question 5

Which of the following is NOT a polynomial?

Accepted Answer

2x^(1/2) - 5

Answer

x^2 - 2x + 1

Answer

x^3 + 2x^2 - 1

Answer

x - 3

Question 6

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 3)^2

Answer

Cannot be factored

Question 7

Which of the following is a polynomial of degree 3?

Accepted Answer

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

Answer

x^2 + 2x

Answer

(x - 1)^3

Answer

x

Question 8

Simplify the expression: (x - 2)/(x + 2) * (x + 2)/(x - 2)

Accepted Answer

1

Answer

0

Answer

-1

Answer

x

Question 9

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

Accepted Answer

-3

Answer

2

Answer

-5

Answer

1

Question 10

Which of the following polynomials is in factored form?

Accepted Answer

(x - 1)(x + 2)

Answer

x² + 2x + 1

Answer

x(x² - 1)

Answer

2x² - 3x + 1

Question 11

Simplify the polynomial expression: (x² - 1)²

Accepted Answer

x⁴ - 2x² + 1

Answer

x⁴ + 2x² + 1

Answer

x² - 2x + 1

Answer

x² + 2x + 1

Question 12

Which of the following expressions is a polynomial?

Accepted Answer

(x - 3)(x + 2)

Answer

sin(x)

Answer

(x^(1/2) + 1)

Question 13

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

Accepted Answer

3

Answer

4

Answer

5

Answer

2

Question 14

Find the remainder when the polynomial: x^3 + 2x^2 - 5x + 3 is divided by x + 1

Accepted Answer

1

Answer

0

Answer

3

Answer

2

Question 15

Which of the following is a rational polynomial?

Accepted Answer

x^3/(x - 2)

Answer

e^x

Answer

sin(x)

Answer

x^(1/2) + 1

Question 16

Factor the polynomial: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)²

Answer

(x + 9)(x - 9)

Answer

The polynomial cannot be factored.

Question 17

Which of the following is NOT a theorem related to polynomials?

Accepted Answer

The Fundamental Theorem of Calculus

Answer

The Factor Theorem

Answer

The Remainder Theorem

Answer

The Rational Root Theorem

Question 18

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

Accepted Answer

2

Answer

3

Answer

-1

Answer

-5

Question 19

Which of the following is a graph of the polynomial: y = x^2 - 4?

Accepted Answer

A parabola opening upwards

Answer

A circle

Answer

A straight line

Answer

A hyperbola

Question 20

Factor the polynomial: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

Cannot be factored

Answer

(x + 3)²

Answer

(x - 3)²

Question 21

Which of the following is NOT a standard form of a polynomial?

Accepted Answer

5x + 2x² - 1

Answer

-x² + 3x - 2

Answer

2x⁴ - 5x³ + 7x² - 3x + 1

Answer

x³ - 2x² + x + 5

Question 22

What is the degree of the polynomial 3x⁵ - 2x³ + 5x - 1?

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Question 23

Which of the following is a polynomial function?

Accepted Answer

f(x) = x³ - 2x² + 5x - 1

Answer

f(x) = e^x

Answer

f(x) = sin(x)

Answer

f(x) = |x|

Question 24

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

Accepted Answer

3

Answer

5

Answer

4

Answer

2

Question 25

Identify the leading coefficient of the polynomial: -3x^4 + 2x^3 - 5x + 1

Accepted Answer

-3

Answer

2

Answer

-5

Answer

5

Question 26

Which of the following is a trinomial?

Accepted Answer

x^2 - 5x + 6

Answer

x + y + z

Answer

2x^3 - x^2 + 3

Answer

x^2 + 5x

Question 27

Simplify the polynomial (x + 2)(x - 3).

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 5x + 6

Answer

2x^2 - x - 6

Question 28

Factor the polynomial x^2 - 4.

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 2)^2

Answer

(x + 2)^2

Answer

(x - 4)(x + 1)

Question 29

Find the value of (x - 2)^3 when x = 3.

Accepted Answer

27

Answer

125

Answer

64

Question 30

Which of the following is the degree of the polynomial 2x^4 - 3x^2 + 5?

Accepted Answer

4

Answer

2

Answer

3

Answer

1

Question 31

Simplify the polynomial (x + 2)^2 - (x - 1)^2.

Accepted Answer

4x + 3

Answer

2x + 3

Answer

4x - 3

Answer

2x - 3

Question 32

Which of the following is NOT a polynomial?

Accepted Answer

1/x

Answer

x^(1/2) + 3

Answer

2x^3 - 5x + 1

Answer

x^2 + 2x - 3

Question 33

Find the remainder when the polynomial x^3 - 2x^2 + 5x - 6 is divided by (x - 2).

Accepted Answer

2

Answer

-2

Answer

4

Answer

0

Question 34

Which of the following is the leading coefficient of the polynomial -2x^5 + 3x^3 - x + 5?

Accepted Answer

-2

Answer

-1

Answer

3

Answer

5

Question 35

Which of the following is the constant term of the polynomial 2x^4 - 3x^2 + 5x - 6?

Accepted Answer

-6

Answer

-3

Answer

2

Answer

5