Key Features of Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

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 zero of a polynomial to 'bounce' off the x-axis?

Back

A zero of a polynomial 'bounces' off the x-axis if it has an even multiplicity, meaning the graph touches the x-axis at that point but does not cross it.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial's graph. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

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

Back

The number of roots of a polynomial can be determined by its degree, which indicates the maximum number of roots it can have.

Front

What is a relative maximum in the context of polynomial graphs?

Back

A relative maximum is a point on the graph of a polynomial where the function value is higher than the values of the function at nearby points.

Front

What is an absolute minimum?

Back

An absolute minimum is the lowest point on the entire graph of a polynomial, meaning it has the smallest function value compared to all other points.

Front

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

Back

A polynomial has an even degree if the highest power of the variable is an even number, which affects the end behavior of the graph.

Front

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

Back

A polynomial has an odd degree if the highest power of the variable is an odd number, which results in the graph having opposite end behaviors.

Front

What is the difference between a relative minimum and an absolute minimum?

Back

A relative minimum is lower than nearby points, while an absolute minimum is the lowest point on the entire graph.