# Algebra II

Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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# Polynomial and rational functions

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
All content in “Polynomial and rational functions”

Just saying the word "quadratic" will make you feel smart and powerful. Try it. Imagine how smart and powerful you would actually be if you know what a quadratic is. Even better, imagine being able to completely dominate these "quadratics" with new found powers of factorization. Well, dream no longer. This tutorial will be super fun. Just bring to it your equation solving skills, your ability to multiply binomials and a non-linear way of thinking!

## 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!

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" 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." :)

## Dividing polynomials

You know what polynomials are. You know how to add, subtract, and multiply them. Unless you are completely incurious, you must be wondering how to divide them! In this tutorial we'll explore how we divide polynomials--both through algebraic long division and synthetic division. (We like classic algebraic long division more since you can actually understand what you're doing.)

## Synthetic division

In this tutorial, we'll learn a technique for dividing one polynomial by another--synthetic division. As always, we'll also explore why it works!

## Polynomial remainder theorem

You can always calculate a remainder when you divide one polynomial by another through algebraic long division. As we'll see, however, the polynomial remainder theorem, provides a shortcut when you are dividing a polynomial p(x) by an expression of the form '(x-a)'. In that case, the remainder will just by p(a) (by the polynomial remainder theorem)

## Factoring and roots of higher degree polynomials

Factoring quadratics are now second nature to you. Even when traditional factoring is difficult, you know about completing the square and the quadratic formula. Now you're ready for something more interesting. Well, as you'll see in this tutorial, factoring higher degree polynomials is definitely the challenge you're looking for!

## Polynomial graphs and end behavior

In this tutorial, we will study the behavior of polynomials and their graphs. In particular, we'll look at which forms of a polynomial are best for determining various aspects of its graph.

## 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.

## Rational functions

Have you ever wondered what would happen if you divide one polynomial by another? What if you set that equal to something else? Would it be as unbelievably epic as you suspect it would be?

## 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).