Polynomial Operations and Graphing Quiz

Test your knowledge with polynomial algebra questions including degree, factors, graphs, and more. Get ready for your exams!

Practice Learn Test

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

Which of the following is a polynomial function?

f(x) = 1/x

f(x) = √x

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

f(x) = |x|

Which of the following graphs represents a polynomial function of degree 2?

A parabola opening downward

A straight line

A cubic curve

A parabola opening upward

Which of the following expressions represents a monomial?

3x^2 + 2x + 5

4x^2 + 7x - 3

5x^3 + 2x^2 - 6x + 1

2x^4

What is the product of (x - 3) and (x + 4)?

x^2 - 7x - 12

x^2 + 7x + 12

x^2 - x - 12

x^2 + x - 12

Which property of addition of polynomials is illustrated by the expression (2x^3 + 5x^2) + (3x^3 - 2x^2)?

Associative Property

Commutative Property

Distributive Property

Identity Property

What is the sum of (4x^2 - 3x + 1) and (2x^2 + 5x - 2)?

6x^2 + 2x - 1

6x^2 + 8x - 1

6x^2 + 2x + 3

6x^2 + 2x - 3

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

2x^2 + 7x + 2

2x^2 + 7x - 8

2x^2 - x + 2

2x^2 - x - 8

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

-2

-4

#10

What is the degree of the zero polynomial?

Undefined

Depends on the context

#11

Which of the following statements about polynomial division is true?

The divisor cannot be a polynomial of degree 0.

The quotient can have a degree greater than the dividend.

The remainder must have a degree less than the divisor.

Polynomial division is only defined for monic polynomials.

#12

Which of the following is a factor of the polynomial f(x) = x^3 - 5x^2 + 6x - 30?

(x - 5)

(x - 2)

(x + 5)

(x + 2)

#13

Which of the following is the correct factorization of the polynomial f(x) = x^4 - 16?

(x - 4)(x + 4)

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

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

(x - 8)(x + 8)

#14

If f(x) = 2x^3 - 5x^2 + 3x - 1, what are the zeros of the function?

1, 2

-1, 1/2

3, -1/2

1, -1/2

#15

What is the end behavior of the polynomial function g(x) = -2x^5 + 3x^3 - 4x^2 + 7?

As x approaches positive infinity, g(x) approaches negative infinity, and as x approaches negative infinity, g(x) approaches positive infinity.

As x approaches positive infinity, g(x) approaches positive infinity, and as x approaches negative infinity, g(x) approaches negative infinity.

As x approaches positive infinity, g(x) approaches negative infinity, and as x approaches negative infinity, g(x) approaches negative infinity.

As x approaches positive infinity, g(x) approaches positive infinity, and as x approaches negative infinity, g(x) approaches positive infinity.

#16

Which theorem guarantees that a polynomial of degree n has exactly n roots?

Fundamental Theorem of Algebra

Intermediate Value Theorem

Rational Root Theorem

Factor Theorem

#17

Which of the following is the correct factorization of the polynomial f(x) = x^3 - 8?