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