If a polynomial \( f(x)=x^{4}-2 x^{3}+3 x^{2}-a x-b \) leaves remainders 5 and 19 when divided b...

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If a polynomial \( f(x)=x^{4}-2 x^{3}+3 x^{2}-a x-b \) leaves remainders 5 and 19 when divided by \( (x-1) \) and \( (x+1) \) respectively, find the values of \( a \) and \( b \). Hence, determine the remainder when \( f(x) \) is divided by \( (x-2) \)
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