In Algebra II, a polynomial function is one in which the coefficients are all real numbers, and the exponents on the variables are all whole numbers. A polynomial whose greatest power is 2 is called a *quadratic polynomial**;* if the highest power is 3, then it’s called a *cubic polynomial**.* A highest power of 4 earns the name *quartic* (not to be confused with quadratic), and a highest power of 5 is called *quintic**.*

When solving polynomial functions and equations, don’t let these common mistakes trip you up:

Forgetting to change the signs in the factored form when identifying x-intercepts

Making errors when simplifying the terms in f(–x) applying Descartes’ rule of sign

Not changing the sign of the divisor when using synthetic division

Not distinguishing between curves that cross from those that just touch the x-axis at an intercept

Graphing the incorrect end-behavior on the right and left of the graphs