These are important terms and notations for this section.

We know an awful lot about polynomials, but it relies on the very specific structure of a polynomial, and thus it is paramount that one can correctly recognize what is, and isn’t, a polynomial to use these tools.

This section covers one of the most important results in the last couple centuries in algebra; the so-called “Fundamental Theorem of Algebra.”

This section is a quick foray into math history, and the history of polynomials!

This section contains a demonstration of how odd versus even powers can effect extrema.

This section contains information on how exponents effect local extrema

This section shows and explains graphical examples of function curvature.

Some information on factoring before we delve into the specifics.

We discuss step 0 of factoring, extracting any common factors to simplify the process going forward.

First dive into factoring polynomials. This section covers factoring quadratics with leading coefficient of $1$ by factoring the coefficients.

Factor higher polynomials by grouping terms

How to factor when the leading coefficient isn’t one.

Factor polynomials quickly when they are in special forms

This section introduces the technique of completing the square.

In this section we explore how to factor a polynomial out of another polynomial using polynomial long division

Factor one polynomial by another polynomial using polynomial synthetic division

Find factors via rational root theorem

Intro to complex numbers and conjugates

Simplifying complex numbers

Exploring the usefulness and (mostly) non-usefulness of the quadratic formula

A Comprehensive Factoring Practice Quiz.

These are important terms and notations for this section.

This section introduces radicals and some common uses for them.

This section discusses how to simplify numeric and odd root-value radicals.

This section discusses some of the complications that arise when simplifying radicals.

This section views the square root function as an inverse function of a monomial. This is used to explain the dreaded $\pm$ symbol and when to use (and not use) absolute values.

This section shows techniques to solve an equality that has a radical that can’t be simplified into a non radical form. This has potential drawbacks which is also covered in this section.

These are important terms and notations for this section.

This section introduces inequalities and what they are (and aren’t!)

This section discusses how to compute and/or verify inequalities

This section discusses how to algebraically manipulate inequalities.

This section discusses how to solve inequalities.

This section discusses how to graph linear and non-linear inequalities