Difference between revisions of "Simon's Favorite Factoring Trick"
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* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=454191#p454191 AIME 1987/5] | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=454191#p454191 AIME 1987/5] | ||
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== See Also == | == See Also == |
Revision as of 15:05, 17 July 2006
Contents
[hide]Introduction
Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization first popularized by AoPS user Simon Rubinstein-Salzedo. This appears to be the thread where Simon's favorite factoring trick was first introduced.
Statement of the factorization
The general statement of SFFT is: . Two special cases appear most commonly:
and
.
Applications
This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually and
are variables and
are known constants. Also it is typically necessary to add the
term to both sides to perform the factorization.