To factor the quadratic expression \(x^2 - 3x - 28\), we need to find two numbers that multiply to \(-28\) (the constant term) and add up to \(-3\) (the coefficient of \(x\)).
The two numbers that satisfy these conditions are \(4\) and \(-7\) because:
- \(4 \times -7 = -28\)
- \(4 + (-7) = -3\)
Using these numbers, we can factor the expression:
\[ x^2 - 3x - 28 = (x + 4)(x - 7) \]
Thus, the factored form of \(x^2 - 3x - 28\) is:
\[ (x + 4)(x - 7) \]