Polynomial Function Quiz

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

• 5

• 3

• 4

• 2

Define a polynomial function.

• A polynomial function is a function that involves only one variable.

• A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_{n-1}*x^{n-1} + ... + a_1*x + a_0

• A polynomial function is a function that has a constant value.

• A polynomial function is a function that can only be graphed as a straight line.

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

• -4

• 3

• -2

• 0

Explain the concept of roots of a polynomial function.

• The roots of a polynomial function are the values of the variable that make the function equal to zero.

• The roots of a polynomial function are the values of the variable that make the function negative.

• The roots of a polynomial function are the values of the variable that make the function undefined.

• The roots of a polynomial function are the values of the variable that make the function positive.

Simplify the expression h(x) = 2x^3 + 5x^2 - 3x - 1.

• h(x) = 2x^3 + 5x^2 - 3x - 1

• h(x) = 2x^3 + 5x^2 - 3x + 1

• h(x) = 2x^3 - 5x^2 - 3x - 1

• h(x) = 2x^3 + 5x^2 + 3x - 1

How can you determine the end behavior of a polynomial function?

• Count the number of terms in the polynomial function.

• Check the symmetry of the polynomial function.

• Look at the degree and leading coefficient of the polynomial function.

• Look at the y-intercept of the polynomial function.

Factorize the polynomial j(x) = x^2 - 4x + 4.

• (x - 1)^2

• (x + 2)^2

• (x - 2)^2

• (x - 3)(x - 1)

What is the difference between a linear and quadratic polynomial function?

• A linear function has a higher degree than a quadratic function

• The main difference is that a quadratic function has a squared term (x^2) which makes it a parabolic curve, while a linear function is a straight line.

• A quadratic function is always positive, while a linear function can be negative

• A linear function has a vertex, while a quadratic function does not

Find the sum of the roots of the polynomial k(x) = x^2 - 6x + 9.

• 6

• 9

• 12

• 3

Explain the relationship between the roots and factors of a polynomial function.

• The roots of a polynomial function are the highest degree terms in the polynomial

• The roots of a polynomial function are the solutions to the equation obtained by setting the polynomial equal to zero, and these roots correspond to the factors of the polynomial.

• The factors of a polynomial function are the solutions to the equation obtained by setting the polynomial equal to zero

• The roots of a polynomial function are always imaginary numbers