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The remainders of the polynomial $f (x)$ when divided by $x + 1, x + 2, x - 2$ are $6, 15, 3$ the remainder of $f (x)$ when divided by $(x + 1) (x + 2) (x - 2)$ is

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$2 x^{2} - 3 x + 1$

$3 x^{2} - 2 x + 1$

$2 x^{2} - x - 3$

$3 x^{2} + x - 3$

answer is A.

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Detailed Solution

$r (x) = a x^{2} + b x + c; r (- 1) = 6, r (- 2) = 15, r (2) = 3$

the required equation is $2 x^{2} - 3 x + 1$

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