To factor the quadratic expression \( x^2 - 2x - 15 \), we need to find two numbers that multiply to \( -15 \) (the constant term) and add up to \( -2 \) (the coefficient of the linear term).
The two numbers that satisfy these conditions are \( -5 \) and \( 3 \) since:
- \( -5 \times 3 = -15 \)
- \( -5 + 3 = -2 \)
Now we can write the factored form of the expression:
\[ x^2 - 2x - 15 = (x - 5)(x + 3) \]
Thus, the factored form of \( x^2 - 2x - 15 \) is \((x - 5)(x + 3)\).