Khan Academy on a Stick
Polynomial and rational functions
Exploring quadratics and higher degree polynomials. Also indepth look at rational functions.

Factoring quadratic expressions
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Factoring Quadratic Expressions

Examples: Factoring simple quadratics
A few examples of factoring quadratics

Example 1: Solving a quadratic equation by factoring
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U09_L2_T2_we1 Solving Quadratic Equations by Factoring.avi

Example 2: Solving a quadratic equation by factoring
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U09_L2_T2_we2 Solving Quadratic Equations by Factoring 2.avi

Example 1: Factoring trinomials with a common factor
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Factoring trinomials with a common factor

Factoring Special Products
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Factoring Special Products

Example 1: Factoring difference of squares
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Factoring difference of squares

Example 2: Factoring difference of squares
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Factoring difference of squares
 Factoring to produce difference of squares

Example 5: Factoring by grouping
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Factoring Trinomials by Grouping 5

Example 6: Factoring by grouping
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Factoring Trinomials by Grouping 6
Factoring quadratics
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 nonlinear way of thinking!

Solving Quadratic Equations by Square Roots
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Solving Quadratic Equations by Square Roots

Solving Quadratic Equations by Completing the Square
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Solving Quadratic Equations by Completing the Square

How to use the Quadratic Formula
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Introduction to using the quadratic formula.

Proof of Quadratic Formula
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Proof of Quadratic Formula

Example: Complex roots for a quadratic
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Complex Roots from the Quadratic Formula

Discriminant of Quadratic Equations
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Discriminant of Quadratic Equations

Discriminant for Types of Solutions for a Quadratic
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Discriminant for Types of Solutions for a Quadratic
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!

Quadratic Inequalities
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Solving quadratic inequalities using factoring

Quadratic Inequalities (Visual Explanation)
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How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means.
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.

Terms coefficients and exponents in a polynomial
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Terms coefficients and exponents in a polynomial

Addition and Subtraction of Polynomials
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Addition and Subtraction of Polynomials

Multiplying Polynomials
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Multiplying Polynomials

Multiplying Polynomials 3
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Multiplying Polynomials 3

Polynomial Division
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Polynomial Division

Dividing polynomials 1
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Dividing polynomials 1

Dividing polynomials with remainders
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Dividing polynomials with remainders

Synthetic Division
Basic algorithm for Synthetic Division

Synthetic Division Example 2
Another example of applying the basic synthetic division algorithm

Why Synthetic Division Works
Demonstrating why synthetic division gives you the same result as traditional algebraic long division

Factoring Sum of Cubes
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Factoring Sum of Cubes

Difference of Cubes Factoring
u12 l2 t3 we2 Difference of Cubes Factoring
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 (part 1)
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Introduction to raising (a+b)^n

Binomial Theorem (part 2)
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Binomial Theorem and Pascal's Triangle

Binomial Theorem (part 3)
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Intuition behind why binomial expansion involves combinatorics
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 Introduction
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Simplifying Rational Expressions

Simplifying Rational Expressions 1
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U11_L1_T1_we1 Simplifying Rational Expressions 1

Simplifying Rational Expressions 2
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U11_L1_T1_we2 Simplifying Rational Expressions 2

Simplifying Rational Expressions 3
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U11_L1_T1_we3 Simplifying Rational Expressions 3
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.

Adding and Subtracting Rational Expressions
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Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions 2
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U11_L1_T3_we2 Adding and Subtracting Rational Expressions 2

Adding and Subtracting Rational Expressions 3
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U11_L1_T3_we3 Adding and Subtracting Rational Expressions 3

Rational Equations
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Rational Equations

Solving Rational Equations 1
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Solving Rational Equations 1

Solving Rational Equations 2
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Solving Rational Equations 2

Solving Rational Equations 3
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Solving Rational Equations 3

Subtracting Rational Expressions
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Subtracting Rational Expressions

Applying Rational Equations 1
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Applying Rational Equations 1

Applying Rational Equations 2
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Applying Rational Equations 2

Applying Rational Equations 3
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Applying Rational Equations 3

Multiplying and Simplifying Rational Expressions
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Multiplying and Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions 1
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Multiplying and Dividing Rational Expressions 1

Multiplying and Dividing Rational Expressions 2
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Multiplying and Dividing Rational Expressions 2

Multiplying and Dividing Rational Expressions 3
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Multiplying and Dividing Rational Expressions 3

Extraneous Solutions to Rational Equations
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Extraneous Solutions to Rational Equations

Rational Inequalities
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Two ways to solve a rational inequality (or an inequality involving a fractional expression)

Rational Inequalities 2
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Slightly harder rational inequality problem
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?

Asymptotes of Rational Functions
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Asymptotes of Rational Functions

Another Rational Function Graph Example
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Another Rational Function Graph Example

A Third Example of Graphing a Rational Function
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A Third Example of Graphing a Rational Function
Asymptotes and graphing rational functions

Partial Fraction Expansion 1
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Introduction to partial fraction expansion

Partial Fraction Expansion 2
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A more complex problem

Partial Fraction Expansion 3
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Dealing with repeated factors
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 leastcommon multiple of the lowerdegree ones). This tutorial lets us think about going the other waystart 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).