Although polynomial functions can include functions with any degree that is a nonnegative integer, here we are focusing on those with degree 3 or higher since we've already looked at linear and quadratic function families. We will focus primarily on cubic functions, but also take a look at quartic, quintic, and others.

A polynomial function can be represented in the same four ways we learned in Unit 1: graph, table, equation, verbal description.

We can calculate average rates of change between any two points on a polynomial function just like we learned in Unit 1.

We can also determine the key features of a graph of a polynomial: domain, range, x and y-intercepts, increasing/decreasing intervals, absolute and relative maximums/minimums.

End behavior describes how the two ends of a polynomial graph behave in relation to its degree.

Even functions are symmetrical about the y-axis. Odd functions are symmetrical about the origin.

Polynomials can be factored similar to quadratics in order to reveal "factored form." The advantage of factored form (just like in the quadratic family) is that we can see what the real roots or zeros of the function will be. From these zeros we can then sketch a rough graph of the polynomial without the need of a calculator.

Polynomials that bounce off the x-axis are said to have an even "multiplicity" at that zero. Polynomials that cross the x-axis are said to have an odd "multiplicity" at that zero.

Long division of polynomials is useful for revealing whether an expression is truly a factor of a polynomial or not. If the remainder is zero, then it is a factor, and we can find a zero (or root) from it.

Similarly, the Remainder Theorem tells us that when dividing any polynomial by a linear factor (x-r) the remainder will be the y-value, f(r). In other words, if we plug r into the polynomial function and the output f(r) = 0 then (x - r) is a true factor of that polynomial.

Polynomial functions can be solved for their zeros algebraically or graphically.