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Topic: Factoring
Replies: 52   Last Post: Jan 16, 2012 8:23 PM

 Messages: [ Previous | Next ]
 Dave L. Renfro Posts: 4,792 Registered: 12/3/04
Re: Factoring
Posted: Jan 12, 2012 10:50 AM

Dave L. Renfro wrote:

>> Back in August 2010 I posted a .pdf file of a handout I wrote
>> for a high school precalculus class that I taught several
>> times in the mid to late 1990s. However, I used the result
>> to prove various irrationality results, which I thought was
>> a more mathematically important and interesting application.
>> Moreover, coming up with the polynomials to apply the rational
>> root theorem to helped students practice algebraic manipulation
>> skills, which I also thought was a more mathematically important
>> skill than using the theorem to factor contrived polynomials.
>>
>> You can find the .pdf file at

http://mathforum.org/kb/message.jspa?messageID=6886991

John Smith wrote:

> Thanks I just printed it.

Given your interest in this topic, here are some more items you
might be interested in. At the beginning of the integration
handouts (first item below) I give several "high school" ways
to factor 1 + x^4, 1 + x^5, and 1 + x^6. The sci.math post
"Integrating Rational Functions" also has some relevant aspects,
such as a proof (assuming the Fundamental Theorem of Algebra)
that every polynomial with real coefficients can be factored
into polynomials with real coefficients whose degrees are at
most 2.

Handouts on integrating 1/(1 + x^n) for n = 4, 5, 6
http://mathforum.org/kb/message.jspa?messageID=6868513

Handouts on the Factor Theorem
http://mathforum.org/kb/message.jspa?messageID=7643514

sci.math post: "Integrating Rational Functions" [15 April 2006]

A very detailed solution (in "square root form") to x^17 = 1
http://pballew.net/Constructable_17gon.pdf

sci.math post: "Some turbo-charged high school algebra" [21 August
2008]