Exploration of Functions
1Polynomial Functions
This section is an exploration of polynomial functions, their uses and their
mechanics.
1.2What is (and isn’t) a Polynomial?
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.
1.4Fundamental Theorem of Algebra
This section covers one of the most important results in the last couple centuries in
algebra; the so-called “Fundamental Theorem of Algebra.”
1.6An Interjection into Polynomial History!
This section is a quick foray into math history, and the history of polynomials!
1.7Exponents and Extrema: An Example
This section contains a demonstration of how odd versus even powers can effect
extrema.
1.9Exponents and Extrema 2: Local Extrema
This section contains information on how exponents effect local extrema
1.13Factoring: Common Factors
We discuss step 0 of factoring, extracting any common factors to simplify the process going forward.
1.14Factoring: Round One!
First dive into factoring polynomials. This section covers factoring quadratics with
leading coefficient of by factoring the coefficients.
1.24Polynomial Long Division
In this section we explore how to factor a polynomial out of another polynomial using polynomial long division
1.25Polynomial Synthetic Division
Factor one polynomial by another polynomial using polynomial synthetic division
2Radical Functions
This section is an exploration of radical functions, their uses and their mechanics.
2.3Simplifying Radicals - Part 1
This section discusses how to simplify numeric and odd root-value radicals.
2.5Simplifying Radicals - Part 2
This section discusses some of the complications that arise when simplifying radicals.
2.7Square Root: the Inverse Function
This section views the square root function as an inverse function of a monomial. This is used to explain the dreaded symbol and
when to use (and not use) absolute values.