Difference between revisions of "Factoring"

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===Why Factor===
 
===Why Factor===
Factoring equations is an essintial part of problem solving. Applying number theory to products yields many results.
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Factoring equations is an essential part of problem solving. Applying number theory to products yields many results.
  
 
There are many ways to factor.
 
There are many ways to factor.

Revision as of 06:43, 19 June 2006

Note to readers and editers: Please fix up this page by adding in material from Joe's awesome factoring page.


Why Factor

Factoring equations is an essential part of problem solving. Applying number theory to products yields many results.

There are many ways to factor.

Difference of Squares

$a^2-b^2=(a+b)(a-b)$

Difference of Cubes

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Sum of Cubes

$a^3+b^3=(a+b)(a^2-ab+b^2)$

Simon's Trick

See Simon's Favorite Factoring Trick (This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)

Summing Series

Also, it is helpful to know how to sum arithmetic series and geometric series.

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