Polynomial Functions and Algebraic Operations Quiz

Test your understanding of polynomial algebra with questions on degrees, factors, roots, and operations. Try now!

Practice Learn Test

What is the degree of the polynomial function f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 9?

Which of the following is a factor of the polynomial f(x) = x^3 - 4x^2 + x + 6?

x - 2

x + 2

x - 3

x + 3

Which of the following is a factor of the polynomial f(x) = x^4 - 6x^3 + 11x^2 - 6x + 1?

x - 1

x - 2

x - 3

x - 4

What are the roots of the equation 2x^2 - 5x - 3 = 0?

1, -3

3, -1

1, 3

-1, -3

Which of the following is NOT a polynomial function?

f(x) = 2x^3 - 5x^2 + 4x - 1

g(x) = √(x^2 + 1)

h(x) = 4x^2 - 3x + 2

k(x) = x^6 - 9x^3 + 2

What is the leading coefficient of the polynomial f(x) = 6x^4 - 3x^3 + 2x^2 - 5x + 7?

-3

What is the degree of the polynomial function f(x) = 2x^6 + 5x^4 - x^3 + 3?

What is the sum of the roots of the equation x^2 - 5x + 6 = 0?

If f(x) = 2x^3 + 5x^2 - 4x + 7 and g(x) = x^2 - 3x + 2, what is f(x) / g(x)?

2x + 1

2x^2 + x + 3

2x - 1

2x^2 - x + 3

#10

If f(x) = 3x^3 - 4x^2 + 2x - 5 and g(x) = x^2 + 2x + 3, what is f(x) * g(x)?

3x^5 + 2x^4 - 2x^3 - 16x^2 + 4x - 15

3x^5 - 4x^4 - 2x^3 + 8x^2 + 10x - 15

3x^5 - 4x^4 - 2x^3 - 16x^2 + 4x - 15

3x^5 + 2x^4 - 2x^3 + 8x^2 + 10x - 15

#11

What is the quotient when the polynomial f(x) = 4x^3 - 9x^2 + 7x + 6 is divided by (x + 2)?

4x^2 - 17x + 34

4x^2 - 17x + 30

4x^2 - 5x + 17

4x^2 - 5x + 34

#12

If f(x) = x^5 - 4x^4 + 6x^3 + 2x^2 - x + 9 and g(x) = x^3 - 2x^2 + 3x + 1, what is f(x) - g(x)?

x^5 - 4x^4 + 6x^3 + x^2 - 4x + 8

x^5 - 4x^4 + 5x^3 + x^2 - 2x + 10

x^5 - 4x^4 + 4x^3 - x^2 + 2x + 8

x^5 - 4x^4 + 6x^3 - 3x^2 - 2x + 8

#13

What is the quotient when the polynomial f(x) = 3x^4 - 5x^3 + 7x^2 - x + 2 is divided by (x - 1)?

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

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

3x^3 - 6x^2 + 7x - 1

3x^3 - 6x^2 + 7x - 3

#14

If f(x) = 2x^4 - 3x^3 + 4x^2 - 5x + 6 and g(x) = x^2 - 2x + 3, what is f(x) + g(x)?

2x^4 - 3x^3 + 5x^2 - 7x + 9

2x^4 - 3x^3 + 6x^2 - 3x + 9

2x^4 - 3x^3 + 6x^2 - 7x + 9

2x^4 - 3x^3 + 5x^2 - 3x + 9

#15

What is the remainder when the polynomial f(x) = 2x^4 - 5x^3 + 3x^2 + x - 9 is divided by (x - 3)?

#16

Which of the following is a root of the equation x^3 - 6x^2 + 11x - 6 = 0?

#17

What is the remainder when the polynomial f(x) = 2x^4 - 7x^3 + 3x^2 + 4x - 9 is divided by (x + 2)?

-29

-19

-9

-3

#18

What is the remainder when the polynomial f(x) = x^5 - 3x^4 + 2x^3 + 5x^2 - x + 9 is divided by (x + 3)?

-85

-75

-65

-55

#19

What is the remainder when the polynomial f(x) = 3x^5 - 7x^4 + 4x^3 + 2x^2 - 9x + 5 is divided by (x - 2)?

-11

-5