To factor the quadratic expression \( f^2 - 13f - 14 \), we need to find two numbers that multiply to \(-14\) (the constant term) and add to \(-13\) (the coefficient of \(f\)).
The numbers that satisfy these conditions are \(-14\) and \(1\), since:
\[ -14 \times 1 = -14 \] \[ -14 + 1 = -13 \]
Now we can express the quadratic as a product of two binomials:
\[ f^2 - 13f - 14 = (f - 14)(f + 1) \]
Thus, the factored form of the expression is:
\[ \boxed{(f - 14)(f + 1)} \]