# Glossary for Lesson 20: Factor Theorem

### Higher-Order Polynomial Function

A polynomial function is any function that is defined by a polynomial expression.  The term higher-order polynomial generally refers to a polynomial of degree 3 or higher.  Examples of higher-order polynomial functions include the following: y=x^7 y=-x^3+4x^2+x-8 y=3x^6-8x^2+5 The graphs of polynomial functions are continuous and smooth.

A quadratic function is a polynomial function of degree 2, also known as a second degree polynomial.  It can be written in the form f(x)=ax^2+bx+c , where a , b , and c are constants.  The simplest quadratic function is f(x)=x^2 .

### Left- and Right-Hand Behavior

The left-hand behavior of a function tells us what happens to the value of the function as x tends toward -\inf , way to the left side of the graph. The right-hand behavior of a function tells us what happens to the value of the function as x tends toward \inf , way to the right side of the graph. We can also refer to the right- and left-hand behavior of a graph as its end behavior, since we’re trying to find out what is happening to the ends of the graph. For a polynomial function, as long as it is of degree 1 or greater, the end behavior on either side will either consist of the function rising way up high (approaching \inf ) or falling way down low (approaching -\inf ).