To factor the expression \( x^2 - 2x - 48 \), we need to find two numbers that multiply to \(-48\) (the constant term) and add to \(-2\) (the coefficient of the \(x\) term).
The two numbers that satisfy these conditions are \(6\) and \(-8\), since:
- \(6 \times -8 = -48\)
- \(6 + (-8) = -2\)
Now, we can factor the quadratic expression:
\[ x^2 - 2x - 48 = (x + 6)(x - 8) \]
Thus, the factored form of the expression is:
\[ (x + 6)(x - 8) \]