Study Guide

Polynomials Introduction

Polynomials Introduction

Polynomials. They're functional, sometimes complex, and some would say even otherworldly. We don't know where they would get that last idea, though. We keep coming back to them for whatever reason, and every time we do, we end up learning more about them. This time is no exception. What might we learn? The recipe for their out-of-this-world cookies? How much wood a woodchuck could chuck? Maybe the secrets of life, the universe, and everything?

Probably not on all counts. Sorry if we got your hopes up. But we will find out some other things. Why is the sign of the leading coefficient such a big deal? What exactly happens if we try to divide by zero? What happens when x is gigantic? Or gigantically negative? Will we use complex numbers for anything? Yep, all that and more is waiting for you. And if that isn't incentive enough, we'll share an awesome cookie recipe with you when we finish. How about that as a reward for learning some math?

Polynomials Resources


Real Zeros of Polynomial Functions
Here's a no-nonsense explanation of the roots of polynomial functions. We happen to prefer our nonsense-filled explanation, but we'll take all the help available.

Math Is Fun—Fundamental Theorem of Algebra
Learn the fun-fun-fundamentals of the Fundamental Theorem of Algebra with Math Is Fun. Fun.

Purplemath—The Rational Roots Test
What's scarier than a horde of bees? Not understanding the Rational Root Theorem when test day rolls around. Rub yourself with figurative bee repellant by reading up on the RRT.


PatrickJMT—Synthetic Division Example
Synthetic division can seem artificial if you don't know what's going on. Make some sense of it with Patrick JMT.

PatrickJMT—Long Division of Polynomials
More division help from Patrick, this time on long division. Teach those slant asymptotes a thing or two.

My Secret Math Tutor—Using Descartes' Rule of Signs
Descartes, why is your sign so confusing? Go back to graphic design school.

Upper and Lower Bounds Theorem
Yer out of bounds, zero. Get out of here.

Games and Tools

Factoring Polynomials Calculator
Finds all of the roots of a polynomial, real and complex. We suggest just using it to check your answers. Practice makes perfect, and being perfect at using this calculator won't help that much on the test.

Coolmath: Graphing Polynomials—Multiplicity
For some reason, this page doesn't mention Michael Keaton a single time. Weird.

Wolfram—Rational Function Grapher
A way to graph rational functions with a computer? No, a way to check your rational function graphs. C'mon now, you know better.