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Topic:  Best & New way to teach Long Division 
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Subject:  RE: Best & New way to teach Long Division 
Author:  Howard58 
Date:  Jun 13 2014 
Here is a simple example but any would do:
(x^3 + 3x^2 + 2x +1)/(x^2  4x + 5)
It is OBVIOUS that an attempt to write this as (Ax + B)/(x^24x+5) requires a
linear part as well, call it Cx + D.
So rewrite Cx + D + (Ax + B)/(x^24x+5) as (something)/(x^24x+5), and 4
linear equations appear, in A, B, C and D. Just what is needed to match the
original numerator.
Try with linear factors (x  5)(x  1) in the denominator instead. You still
need the Cx + D, and it is still fairly obvious. Needless to say, the Cx + D is
the quotient of the polynomial division!!!
 
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