The correct option is D −x
As degree of remainder is always lesser than degree of divisor,we have taken remainder with degree less than 2 here.
Let ux+v be the remainder when p(x) is divided by (x2−a2)
Using division algorithm,
where q(x) is the quotient.
We know that, by remainder theorem,
Putting x=a and x=−a in the equation (i),
Solving them simultaneously,
Hence, the required remainder is