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Study Guides > Intermediate Algebra

Why It Matters: Polynomials

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. Dolphin rendered with a mesh of triangles 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.[footnote]Loop, Charles, and Jim Blinn. Real-time GPU Rendering of Piecewise Algebraic Surfaces. ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06 (2006): n. pag. Web.[/footnote].  In this process, the surfaces that are rendered are made from solutions to algebraic polynomials. The image below shows some images of smooth-surfaced objects that were rendered using polynomials by researchers Charles Loop and Jim Blinn from Microsoft.
8 figures rendered with a computer using a polynomial algorithm instead of a triangular mesh. Shapes include a cone, cylinder, sphere, bowling pins, @, a torus and two original shapes. Surfaces Rendered Using Polynomials.
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.

In this module you will learn how to do the following:

  • Define and evaluate polynomials over the real numbers
  • Perform algebraic operations on polynomials
  • Define and evaluate polynomial functions
  • Recognize key features of polynomial graphs
  • Perform algebraic operations on polynomial functions

Licenses & Attributions

CC licensed content, Original

  • Screenshot Polynomial Generated Images. Provided by: Lumen Learning License: CC BY: Attribution.
  • Why it Matters: Polynomials. Provided by: Lumen Learning License: CC BY: Attribution.
  • Graphic: Module 5 concepts you need. Provided by: Lumen Learning License: CC BY: Attribution.

CC licensed content, Shared previously

  • Dolphin Triangle Mesh. Authored by: By en:User:Chrschn . Located at: https://commons.wikimedia.org/w/index.php?curid=10626667. License: Public Domain: No Known Copyright.