We translate the given information about P into information about a, b and c.
\begin{align*}
P(1) &= 1 \implies a+b+c =1,\\
P(2) &= 2 \implies 4a+2b+c =2,\\
P(3) &= 4 \implies 9a+3b+c =4.
\end{align*}
Subtracting the first equation from the second and the second equation from the third gives
\begin{align*}3a+b&=1,\\
5a+b&=2.
\end{align*}
Subtracting the first equation above from the second gives 2a=1, so a=1/2 and b=-1/2. It then follows that c=1. So, our answer is\
\[\frac{1}{2} - \left(-\frac 12\right) - 1 = \boxed{0}.\]
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