Polynomial Operations and Equations Quiz

Test your knowledge of polynomial algebra with questions on degree, operations, roots, and factors.

Practice Learn Test

What is the degree of the polynomial 3x^2 - 5x + 2?

Not defined

Which of the following is not a polynomial?

3x^2 + 5x - 2

√x + 3

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

4x^3 - 2x + 5

Which of the following is the factor theorem?

If a polynomial f(x) is divided by (x - a), the remainder is f(a).

If a polynomial f(a) is divided by (x - a), the remainder is f(x).

If a polynomial f(a) is divided by (x + a), the remainder is f(x).

If a polynomial f(x) is divided by (x + a), the remainder is f(a).

Which of the following represents a difference of two squares?

x^2 + 5x + 25

x^2 - 25

x^2 + 5x - 25

x^2 - 5x + 25

Which of the following is a factor of the polynomial x^3 + 2x^2 - x - 2?

x - 1

x + 1

x - 2

x + 2

What is the result of the operation (x^2 + 3x - 4) + (2x^2 - 5x + 6)?

3x^2 - 2x + 2

3x^2 - 2x - 2

3x^2 - 2x + 10

3x^2 - 8x + 2

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

Which of the following is a factor of the polynomial x^3 - 8x^2 + 17x - 10?

x - 1

x + 1

x - 2

x + 2

What is the sum of the roots of the polynomial equation x^2 - 6x + 9 = 0?

#10

Which of the following is a solution to the equation 2x^2 - 5x + 3 = 0?

x = 3, x = 1/2

x = 3, x = -1/2

x = 2, x = 3/2

x = -2, x = 3/2

#11

What is the remainder when the polynomial 3x^3 - 5x^2 + 2x + 7 is divided by x - 2?

-9

#12

Which of the following is a solution to the equation x^3 - 5x^2 + 4x + 6 = 0?

-2

#13

What is the product of the roots of the polynomial equation 2x^2 + 5x - 3 = 0?

-3/2

3/2

-3

#14

What is the quotient when (3x^4 - 7x^3 + 2x^2 - 5x + 9) is divided by (x - 3)?

3x^3 - 16x^2 + 50x - 141

3x^3 - 16x^2 + 50x - 150

3x^3 - 16x^2 + 50x - 153

3x^3 - 16x^2 + 50x - 156

#15

What is the product of the roots of the equation x^2 - 9 = 0?

-9

-3