To factor the expression \( s^2 - 3s - 4 \), we need to find two numbers that multiply to \(-4\) (the constant term) and add up to \(-3\) (the coefficient of the linear term).
The two numbers that meet these criteria are \(-4\) and \(1\), since:
- \(-4 \times 1 = -4\)
- \(-4 + 1 = -3\)
Now, we can express the quadratic in factored form:
\[ s^2 - 3s - 4 = (s - 4)(s + 1) \]
Thus, the factored form of \( s^2 - 3s - 4 \) is:
\[ (s - 4)(s + 1) \]