Difference between revisions of "Simon's Favorite Factoring Trick"

 
(Simon's Favorite Factoring Trick)
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=== Simon's Favorite Factoring Trick ===
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=== Statement of the factorization ===
Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: <math>xy+x+y+1=(x+1)(y+1)</math>. This factorization frequently shows up on contest problems, espcially those heavy on algbraic manipulation.
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Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: <math>{xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>.
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=== Applications ===
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This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually <math>{x}</math> and <math>{y}</math> are variables and <math>j,k</math> are known constants. Also it is typically necessary to add the <math>{j}{k}</math> term to both sides to perform the factorization.

Revision as of 16:42, 17 June 2006

Statement of the factorization

Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: ${xy}+{xk}+{yj}+{jk}=(x+j)(y+k)$.

Applications

This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually ${x}$ and ${y}$ are variables and $j,k$ are known constants. Also it is typically necessary to add the ${j}{k}$ term to both sides to perform the factorization.

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