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If the remainder when polynomial
P(x)=2x5+x3−2x2−4x+5\text{P}(x)=2x^5+x^3-2x^2-4x+5P(x)=2x5+x3−2x2−4x+5
is divided by x−1+2x-1+\sqrt{2}x−1+2 can be written as a−bca-b\sqrt{c}a−bc, where aaa, bbb and ccc are positive integers and ccc is square free. Then find a+b+ca+b+ca+b+c.
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