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If the remainders of the polynomial f(x) when divided by x – 1, x – 2 are 2, 5 then the remainder of f(x) when divided by (x–1)(x– 2) is

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1 – x

2x–1

3x–1

answer is D.

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Detailed Solution

$f (x) = (x - 1) (x - 2) + a x + b$

$f (1) = 2 \Rightarrow a + b = 2$

$f (2) = 5 \Rightarrow 2 a + b = 5$

$\Rightarrow a = 3, b = - 1$

Remainder is $\begin{matrix} 3 x - 1 \end{matrix}$ $3 x - 1$

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