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Let $a \neq 0$ and $P (x)$ be a polynomial of degree greater than 2. If $P (x)$ leaves remainder $a and - a$ when divided respectively by $x + a$ and $x - a$ then the remainder when $P (x)$ is divided by $x^{2} - a^{2}$ is

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- 2 x

2 x

x

- x

answer is D.

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Detailed Solution

p (- a) = a

$p (+ a) = - a$

$x^{2} - a^{2}) \underline{p (x)} (^{}$

$?$

$p (x) = (x^{2} - a^{2}) \times q (x) + R (x)$

$p (a) = (0) + R (a)$

$- a = R (a)$

$p (- a) = R (x)$

$R (- a) = a$

$R (a) = - a$

$R (x) = - x$

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