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Re: Factoring
Posted:
Jan 12, 2012 10:50 AM
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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]
http://groups.google.com/group/sci.math/msg/4ba262887e7748dc
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]
http://groups.google.com/group/sci.math/msg/62720599acd91fac
sci.math post: "Factorization of a^3 + b^3 + c^3 - 3abc" [23 April
2009]
http://groups.google.com/group/sci.math/browse_thread/thread/2a5d7849bec3424f
Dave L. Renfro
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