Understanding Polynomial End Behavior and Zeros

Front

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

Back

Degree 4 (quartic)

Front

What describes the leading term of a polynomial with a negative coefficient and even degree?

Back

Negative coefficient, even degree

Front

Analyze the end behavior of the polynomial h(x) = -x^3 + 2x^2 - 4x + 1. As x goes to the left, what happens to h(x)?

Back

h(x) goes up

Front

How many zeros does the polynomial function P(x) = 3x^4 + 4x - 8 have?

Back

4

Front

What is the leading coefficient of a polynomial with a positive leading term?

Back

Positive

Front

Define a polynomial function.

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

Back

As x approaches infinity, f(x) approaches infinity; as x approaches negative infinity, f(x) approaches negative infinity.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the polynomial evaluates to zero.

Front

How can you determine the number of zeros a polynomial can have?

Back

A polynomial of degree n can have at most n real zeros.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the direction of the end behavior of the polynomial.