Can't use $$a^2 - b^2$$

Algebra Level 4

Let $$a$$ be a non-zero real number and $$p(x)$$ be a polynomial of degree greater than 2. If $$p(x)$$ leaves remainder $$a$$ and $$-a$$ respectively by $$x+a$$ and $$x-a$$, the remainder when $$p(x)$$ is divided by $$x^2 - a^2$$ is

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