Polynomial Functions

Front

What is 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 leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the leading coefficient affect the end behavior of a polynomial function?

Back

If the leading coefficient is positive, the polynomial will rise to the right; if negative, it will fall to the right.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial with an even degree will have the same end behavior on both sides (either both ends rise or both ends fall).

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial with an odd degree will have opposite end behaviors (one end rises while the other falls).

Front

What are the linear factors of a polynomial?

Back

Linear factors are expressions of the form (x - r), where r is a root of the polynomial.

Front

How can you determine the number of real roots of a polynomial?

Back

The number of real roots can be determined by analyzing the polynomial's degree and its factors.

Front

What is the significance of the constant term in a polynomial?

Back

The constant term is the value of the polynomial when the variable is zero and can indicate the y-intercept of the graph.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.