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If the remainder when polynomial

$\text{P}(x)=2x^5+x^3-2x^2-4x+5$

is divided by $x-1+\sqrt{2}$ can be written as $a-b\sqrt{c}$, where $a$, $b$ and $c$ are positive integers and $c$ is square free. Then find $a+b+c$.

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