To factor the quadratic expression \( f^2 - 10f - 11 \), we need to find two numbers that multiply to \(-11\) (the constant term) and add up to \(-10\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(-11\) and \(1\) because:
\[ -11 \times 1 = -11 \quad \text{and} \quad -11 + 1 = -10. \]
Now we can rewrite the quadratic expression as follows:
\[ f^2 - 10f - 11 = (f - 11)(f + 1). \]
Thus, the factored form of \( f^2 - 10f - 11 \) is:
\[ (f - 11)(f + 1). \]