To factor the quadratic equation \( x^2 + 4x - 32 = 0 \), we need to find two numbers that multiply to \(-32\) (the constant term) and add to \(4\) (the coefficient of the linear term).
The factors of \(-32\) that add up to \(4\) are \(8\) and \(-4\).
Therefore, we can factor the quadratic as:
\[ (x + 8)(x - 4) = 0 \]
So, the correct factored form is:
\((x + 8)(x - 4) = 0\)