Session 6 (week 3b)

Chapter 2 Polynomials

Section 2.2 Operations on Polynomial Expressions

1. Activities

W. Michael Kelley (2006). The Humongous Book of Calculus Problems.

Complete problems 2.11 - 2.19 [p. 18 - 21]

Wayne W. Dyer (2007). Change Your Thoughts - Change Your Life.

Read Verse 6: Living Creatively [p. 28 - 32]

2. What's it all about?

This section contains 9 problems involving addition, mutiplication, subtraction and division of expressions involving polynomials.

3. What am I able to do, now that I am finished this section?

• I can complete and simplify a polynomial expression involving addition, subtraction, multiplication, and division of polynomials.
• I will be able to carry out polynomial long division.

4. What will I know?

• I will be able to extend what I know about addition, subtraction, multiplication and division to complex polynomials

5. What are the key concepts?

• polynomial long division

6. What are some relevant Web sites for this material?

Using your favorite search engine, and maybe one or two others, type in a few key words such as "polynomial arithmetic" or "polynomial division".

Here are a few Web sites that I liked:

• http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Polynomial.html
• http://www.ltcconline.net/greenl/courses/152a/polyExp/polyarit.htm
• http://www.sosmath.com/algebra/factor/fac01/fac01.html
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut36_longdiv.htm#step1

7. What concept map can I create for this section?

There is no real value in creating a map for this session.

8. What types of Mathematica activities can I create?

Mathematica has a function called Simplify that will perform the algebraic operations, but this does not lead to further understanding of what steps were followed.

It is always fun to test the limits of the software by trying various types of extreme values.

9. What are some connections to other ideas?

The same ideas involving operations with numbers can be extended to operations with abstract entities such as variables.

10. What is my overall reaction to this section?

There is a feeling of control over complex expressions and how they can be simplified, but there is little sense of what the expression may actually look like or why one might be interested in such expressions.

11. Comments on Dyer: 6. Living Creatively

Dyer comments on the sixth verse of the Tao Te Ching as follows: "Lao-tzu refers to an eternal and indescribable force of creation that continuously gives birth to new life." Dyer extends this to include "the birthing of new ideas, new accomplishments, new projects, and new ways of understanding your life". Dyer continues, "Be creative - in your thoughts, in your feelings, and in all of your actions. Apply your own uniqueness to everything you undertake."

This is exactly what this self-study material on calculus is all about. Approach this material your way. Search the Web your way. Browse some Web sites to simply get a sense of what is being said. Play with software such as Mathematica to see what happens. Ask your own questions, even if you have no idea of how to answer them.