Characteristics 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 is a relative maximum?

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 a relative minimum?

Back

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

Front

What is an absolute maximum?

Back

An absolute maximum is the highest point over the entire domain of the polynomial.

Front

What is an absolute minimum?

Back

An absolute minimum is the lowest point over the entire domain of the polynomial.

Front

How can you determine if a polynomial is increasing or decreasing?

Back

A polynomial is increasing on an interval if the derivative is positive on that interval, and decreasing if the derivative is negative.

Front

What does the graph of a polynomial look like?

Back

The graph of a polynomial can have various shapes, including curves and turns, depending on its degree and coefficients.

Front

What is the significance of the x-intercepts of a polynomial?

Back

The x-intercepts of a polynomial are the points where the graph crosses the x-axis, indicating the values of x for which the polynomial equals zero.

Front

What is the significance of the y-intercept of a polynomial?

Back

The y-intercept of a polynomial is the point where the graph crosses the y-axis, indicating the value of the polynomial when x=0.