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Chapter4Polynomials and Factoring

In this chapter, we'll discuss the next level of complexity for equations by allowing our variables to have positive whole numbers as exponents, such as \(x^2+4x+3\) or \(3x^3-2x^2+3x-1\) . Equations with this next level of complexity are examples of Polynomial Equations.

Something cool about polynomials is that most of the functions you can think of in the world, no matter how complicated, can be estimated by polynomial equations! This means that no matter how complicated something is, there is a way to estimate it with just the simple operations of addition, subtraction, multiplication, and positive whole number exponents! The image below shows a jagged complicated function in blue, along with a relatively nicer function in red that approximates it. This is the idea that polynomials can lead to!

You'll also learn in this chapter how to factor some polynomials. Factoring is a key process for solving equations because it lets us know where the function intersects the horizontal axis. Applications could be to find where your equation of revenue "breaks even"!

Polynomial approximation

2012 Wikipedia (Function Approximation)