Explanation:

- First, observe that the expression is \((265)^{4081} + 9\).

- Since we need to find the remainder of this expression divided by 266, it can be simplified using modular arithmetic.

- \(265 \equiv -1 \pmod{266}\), so \((265)^{4081} \equiv (-1)^{4081} \equiv -1 \pmod{266}\).

- Adding 9, we have \((265)^{4081} + 9 \equiv -1 + 9 \equiv 8 \pmod{266}\).

- Thus, the remainder is 8.

Answer: Option 1 - 8