a polynomial has remainder 3 when divided by (x-2) and a remainder of -5 when divided by (x+2) what is the remainder when divided by (x^2-4)?

Let f(x) be the polynomial.
Let Q(x) and (ax + b) be the quotient and the remainder respectively when f(x) is divided by (x² - 4).
Then, f(x) = (x² - 4)•Q(x) + (ax + b)

When f(x) is divided by (x - 2):
The remainder = f(2) = 3
a(2) + b = 3
2a + b = 3 …… [1]

When f(x) is divided by (x + 2):
The remainder = f(-2) = -5
a(-2) + b = -5
-2a + b = -5 …… [2]

[1] - [2]:
4a = 8
a = 2

[1] + [2]:
2b = -2
b = -1

The remainder is (2x - 1) when the polynomial is divided by (x² - 4).