Factoring polynomials -- help an English major!

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Permalink Reply by Geoff St. Pierre on April 30, 2009 at 6:15pm

                 1               1   1
             1   2   1

           1   3   3   1

         1   4   6   4   1

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This is Pascal's Triangle ; which is intriguing and self propagating (recursive) ... a small child can understand it. Life is also self propagating or if not then non existant.

Pascal himself did not invent the triangle but authored some wonderful polynomial connections papers. As a man Pascal was deeply interested in philosophy and religion. These themes could be connected to creation and myths.

Galois comes to mind as well; insolvabillity of the quintic by methods of radical ( a general quintic).

These themes are not directly related to factoring, but certainly related to polynomials. In my experience talking about these themes and people in the math class can help bring the humanity back to math and bring in some of the students who get tired of the numbers, theorems, examples, and proofs.

I will try to think of others.
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Geoff
http://jasperstreet.homeip.net/wiki/index.php/Math

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Permalink Reply by guzman on May 1, 2009 at 12:58am

Consider Fibonacci's numbers,
they'r defined by a(n+2) = a(n+1)+a(n).

Translate this into an equation in x:
x^2 - x -1 =0.

Factor the polynomial and discover an explicit formula for Fibonacci's numbers and an intriguing relationship between
Fibonacci and The Golden Section.

Just an idea. Not systematic, but it may be interesting.

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Permalink Reply by Nancy Bosch on May 1, 2009 at 3:12pm

Here's a good Fibonacci Connection.

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Permalink Reply by Nancy Bosch on May 1, 2009 at 3:16pm

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Permalink Reply by Greg Twitt on May 8, 2009 at 5:22am

I don't know how to link them in to creation myths etc, but here's a tutorial I created on how to factorise a cubic polynomial...

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Permalink Reply by Tom Welch on May 8, 2009 at 6:08am

Thanks Greg, I watched it and it's a really nice explanation of how to do the factoring. I'm curious about your response when kids say "But Mr. Twitt, when am I ever going to use this?" or "Why do we have to learn this?" Your response might give me some other ideas.

Thanks again for taking time to respond, I really appreciate it!

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