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Math

Algebra II

Conceptual videos and worked examples from basic algebra through algebra 2. Includes videos from the former algebra worked examples playlists.
Community Questions
A thumbnail for: Systems of equations and inequalities
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Systems of equations and inequalities

What happens when we have many variables but also many constraints.
A thumbnail for: Functions and their graphs
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Functions and their graphs

Revisiting what a function is and how we can define and visualize one.
A thumbnail for: Polynomial and rational functions
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Polynomial and rational functions

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
A thumbnail for: Rational expressions
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Rational expressions

You have probably been wondering whether our powers of algebraic problem solving break down if we divide by the variable or we have entire expressions in denominator of a fraction. Well, they don't! In this topic, you'll learn how to interpret and manipulate rational expressions (when you have one algebraic expression divided by another)!
A thumbnail for: Exponential and logarithmic functions
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Exponential and logarithmic functions

An look at exponential and logarithmic functions including many of their properties and graphs.
A thumbnail for: Logarithms
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Logarithms

Log-a-what? No, this tutorial is about neither chopped wood nor music (actually logarithms do have applications in music), but it is fascinating nonetheless. You know how to take an exponent. Now you can think about what exponent you have to raise a number to to get another number. Yes, I agree--unstoppable fun for the whole family. No, seriously, logarithms are used everywhere (including to measure earthquakes and sound).
A thumbnail for: Imaginary and complex numbers
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Imaginary and complex numbers

Understanding and solving equations with imaginary numbers.
A thumbnail for: Conic sections
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Conic sections

A detailed look at shapes that are prevalent in science: conic sections
A thumbnail for: Matrices
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Matrices

Understanding and solving matrices.
Polynomial and rational functions
Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.

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.

Adding and multiplying 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." :)

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!

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.

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).

Advanced structure in expressions

This tutorial is all about *really* being able to interpret and see meaning in algebraic expressions--including those that involve rational expressions, exponentials, and polynomials. If you enjoy these ideas and problems, then you're really begun to develop your mathematical maturity.

Fundamental Theorem of Algebra

This tutorial will better connect the world of complex numbers to roots of polynomials. It will show us that when we couldn't find roots, we just weren't looking hard enough. In particular, the Fundamental Theorem of Algebra tells us that every non-zero polynomial in one-variable of degree n has exactly n-roots (although they might not all be real!)