Q.

Let a≠ 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 x2−a2  is

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a

2x

b

–2x

c

x

d

–x

answer is D.

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Detailed Solution

let px=x2-a2 qx+l x+m     now pa=0+la+m=-a           p-a=0+l-a+m=a     since  P(−a)=a,P(a)=−a  solve the above equations we get, l=-1 ,m=0  therefore required remainder = -x
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