To factor the quadratic 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 work are \(4\) and \(-2\) because:
- \(4 \times (-2) = -8\)
- \(4 + (-2) = 2\)
So we can factor the expression as follows:
\[ x^2 + 2x - 8 = (x + 4)(x - 2) \]
Thus, the factored form of the expression \(x^2 + 2x - 8\) is:
\[ (x + 4)(x - 2) \]