5.1: Why It Matters Polynomials
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 51463
Why learn about polynomials?
If you have ever watched a Pixar movie, you have seen computer generated images. A very common method for generating graphics with a computer is to use what is called a wire mesh. You can think of a wire mesh as a grid – like the ones we have used to graph lines – that has been bent and stretched to make a shape we want, as in the image of a dolphin below.
The dolphin in the image was created by plotting points in space to create connected triangles. This method of rendering graphics works well and is in wide use, but it takes a lot of computer memory. Recently, researchers have been investigating the use of polynomials for rendering graphics in part because it demands less memory in the process.^{[1]}. In this process, the surfaces that are rendered are made from solutions to algebraic polynomials. The image below shows some images of smoothsurfaced objects that were rendered using polynomials by researchers Charles Loop and Jim Blinn from Microsoft.
In this module, you will learn how to identify a polynomial and how to perform algebraic operations on them. Like the linear equations and inequalities you learned about earlier, polynomials are useful in many applications of mathematics as well as in other disciplines like biology, economics, and even cryptology. Gaining a basic understanding of their qualities and how the rules of algebra we have learned so far apply to them will help you learn how to use polynomials both inside and out of your math class.
In your next math class you will likely learn how to solve certain kinds of polynomials and how to graph them as well.
Learning Outcomes

Single Variable Polynomials
 Define and evaluate polynomials

Operations on Polynomials
 Add polynomials
 Multiply polynomials
 Subtract polynomials
 Multiply binomials
 Divide by a polynomial

Applications of Polynomials
 Divide by a monomial
 Write polynomials involving perimeter, area, and volume
 Write polynomials involving cost, revenue, and profit
 Loop, Charles, and Jim Blinn. Realtime GPU Rendering of Piecewise Algebraic Surfaces. ACM SIGGRAPH 2006 Papers on  SIGGRAPH '06 (2006): n. pag. Web. ↵