They call it remainder theorem?

Algebra Level 5

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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