If f(x)=x4-2x3+3x2-ax+b is a polynomial such that when it is divided by x-1 and x+1, the remainders are 5 and 19 respectively. Determine the remainder when f(x) is divided by x-2.

If f(x)= $x^{4} - 2 x^{3} + 3 x^{2} - a x + b$ is a polynomial such that when it is divided by x-1 and x+1, the remainders are 5 and 19 respectively. Determine the remainder when f(x) is divided by x-2.

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