This module involves the study of polynomials and polynomial equations. An example of a polynomial is 3x2 − 7x + 2. An example of a polynomial equation is 3x2 − 7x + 2 = 5.

 

The study of solving polynomial equations dates back to 2000 BC when the Babylonians solved quadratic equations. Equations involving exponents of 3 and 4 were not solved until the sixteenth century—3500 years after quadratic equations were solved!

 

Graphic design is a creative process that combines art and technology to communicate ideas to a particular audience. One powerful tool is vector graphics, which are powered by mathematical equations and include polynomial equations. These graphics can be enlarged or reduced to any size, with no loss in detail or sharpness, for use on billboards, business cards, websites, television, and all other forms of media. In this module you will examine the role polynomials can play in graphic design.

 

Can the wave shapes in the image shown be described as a polynomial function?

 

In this module you will solve a special class of polynomial equations—equations in which the polynomial is factorable. Along the way you will discover how to factor polynomials, perform division of polynomials, and sketch their curves without technology.

 

You will investigate the following question: How can the ability to graph and analyze polynomial functions be used in graphic design?

 

To investigate this question, you will focus on the lessons and questions in the table.

 

Lesson	Topic	Lesson Questions
1	Sketching Polynomial Functions	How does the expanded form of a polynomial function help identify the end behaviour of the corresponding graph?
		How does the factored form of a polynomial function help identify the x-intercepts of the corresponding graph?
2	Factoring Polynomials	How is polynomial division related to numeric division?
		How do you know when a number or binomial is a factor of another number or polynomial?
3	Solving Polynomial Equations	How do you solve polynomial equations involving polynomials of degree 3 or higher?
		How are solutions to equations, factors of polynomials, and x-intercepts of graphs related to one another?

 

Module 3 Project: Graphic Design Using Polynomials will focus on polynomials and graphic design. You will be prompted to complete the Module 3 Project as you work through the lessons. You might want to check the Module 3 Project for a sneak peek now.

 

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