Flashcard Polynomial Functions

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the number of roots.

Front

What is a leading term in a polynomial function?

Back

Front

What is a leading coefficient?

Back

Front

How do you determine if a polynomial function is odd or even?

Back

A polynomial is even if all the exponents of its terms are even, and odd if all the exponents are odd. If it has a mix, it is neither.

Front

What are the end behaviors of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term.

Front

What is the significance of the leading term in determining end behavior?

Back

The leading term dictates the end behavior of the polynomial. If the leading coefficient is positive and the degree is even, the ends rise; if odd, one end rises and the other falls.

Front

What does it mean for a polynomial to rise to the left and fall to the right?

Back

This describes the end behavior of a polynomial function where as x approaches negative infinity, the function value increases, and as x approaches positive infinity, the function value decreases.

Front

What is the difference between a polynomial of degree 2 and degree 3?

Back

A polynomial of degree 2 is a quadratic function, which has a parabolic shape. A polynomial of degree 3 is a cubic function, which can have one or two turning points.

Front

What is a root of a polynomial function?

Back

A root of a polynomial function is a value of x that makes the polynomial equal to zero. It represents the x-intercepts of the graph.

Front

How can you find the roots of a polynomial?

Back

Roots can be found using factoring, the quadratic formula, synthetic division, or numerical methods for higher degree polynomials.