To factor the quadratic expression \( w^2 + 24w - 25 \), we need to find two numbers that multiply to \(-25\) (the constant term) and add up to \(24\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(25\) and \(-1\), since \(25 \cdot (-1) = -25\) and \(25 + (-1) = 24\).
Now we can write the expression in factored form:
\[ w^2 + 24w - 25 = (w + 25)(w - 1) \]
Thus, the factored form of the expression is:
\[ (w + 25)(w - 1) \]