To use the Distributive Property to factor the expression \(x^2 - 2x - 8\), we need to find two numbers that multiply to \(-8\) (the constant term) and add to \(-2\) (the coefficient of the linear term).
The two numbers that satisfy these conditions are \(2\) and \(-4\):
- \(2 \times -4 = -8\)
- \(2 + (-4) = -2\)
Now we can express the quadratic \(x^2 - 2x - 8\) in factored form:
\[ x^2 - 2x - 8 = (x + 2)(x - 4) \]
So, the expression equivalent to \(x^2 - 2x - 8\) is:
\((x + 2)(x - 4)\)
Therefore, the correct response is:
(x + 2)(x - 4)