Trigonometry and precalculus
Polynomial and rational functions
Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
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Completing the square and the quadratic formula

You're already familiar with factoring quadratics, but have begun to realize that it only is useful in certain cases. Well, this tutorial will introduce you to something far more powerful and general. Even better, it is the bridge to understanding and proving the famous quadratic formula. Welcome to the world of completing the square!

Graphing quadratics

Tired of lines? Not sure if a parabola is a disease of the gut or a new mode of transportation? Ever wondered what would happen to the graph of a function if you stuck an x² someplace? Well, look no further. In this tutorial, we will study the graphs of quadratic functions (parabolas), including their foci and whatever the plural of directrix is.

Quadratic inequalities

You are familiar with factoring quadratic expressions and solving quadratic equations. Well, as you might guess, not everything in life has to be equal. In this short tutorial we will look at quadratic inequalities.

Polynomials

"Polynomials" sound like a fancy word, but you just have to break down the root words. "Poly" means "many". So we're just talking about "many nomials" and everyone knows what a "nomial" is. Okay, most of us don't. Well, a polynomials has "many" terms. From understanding what a "term" is to basic simplification, addition and subtraction of polynomials, this tutorial will get you very familiar with the world of many "nomials." :)

Binomial theorem

You can keep taking the powers of a binomial by hand, but, as we'll see in this tutorial, there is a much more elegant way to do it using the binomial theorem and/or Pascal's Triangle.

Simplifying rational expressions

You get a rational expression when you divide one polynomial by another. If you have a good understanding of factoring quadratics, you'll be able to apply this skill here to help realize where a rational expression may not be defined and how we can go about simplifying it.

Partial fraction expansion

If you add several rational expressions with lower degree denominator, you are likely to get a sum with a higher degree denominator (which is the least-common multiple of the lower-degree ones). This tutorial lets us think about going the other way--start with a rational expression with a higher degree denominator and break it up as the sum of simpler rational expressions. This has many uses throughout mathematics. In particular, it is key when taking inverse Laplace transforms in differential equations (which you'll take, and rock, after calculus).