



Someone,
somewhere, someday might walk up to you and say ...



Write
an equation where X = 3, X = 2 and X = 0 all make Y = 0. 





How
would you do it? 





Remember
when we talked about stuff like: 





(X  2)(X
+ 5) = 0






We
said that if a bunch of stuff multiplied together gave you zero 


one
of the things HAD to be equal to zero. 


So: 


X  2 =
0 or X + 5 = 0






Then
we solved for X 








So
if X = 2 then (X  2) = 0 and if X = 5 then (X  5) = 0 





Now
we have: 


X = 3, X =
2, and X = 0



being
places where Y = 0






So: 



If X = 3 
(X  3) = 0 



If X = 2 
(X + 2) = 0 



If X = 0 
(X + 0) = 0 





So,
watch closely ... 


(X
 3)(X + 2)(X + 0) = 0






Multiply
out the left side ... 


X^{3}
 X^{2}  6X = 0






We're
looking for the equation that makes Y = 0 


at
those three places. So put in Y for 0 


and
we're done! 


X^{3}
 X^{2}  6X = Y






copyright 2005 Bruce Kirkpatrick 
