Let a `ne` 0 and P(x) be a polynomial of degree greater then 2.If P(x) leaves remianders a and a- when divided, respectively, by x + a and x - a, then find the remainder when P(x) is divided by `x^(2) - a^(2)`.

Explanation

To solve the problem, we need to find the remainder when the polynomial \( P(x) \) is divided by \( x^2 - a^2 \). We know that \( P(x) \) leaves remainders \( a \) and \( -a \) when divided by \( x + a \) and \( x - a \), respectively.

### Step 1: Set up the polynomial remainder
When \( P(x) \) is divided by \( x^2 - a^2 \), the remainder will be of the form:
\[ R(x) = Ax + B \]
where \( A \) and \( B \) are constants to be determined.
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