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 up to \(4\) (the coefficient of the linear term).
The two numbers that meet these criteria are \(8\) and \(-4\), because:
- \(8 \times -4 = -32\)
- \(8 + (-4) = 4\)
Using these numbers, we can factor the quadratic equation as follows:
\[ x^2 + 4x - 32 = (x + 8)(x - 4) = 0 \]
So, the factored form of the equation is:
\[ (x + 8)(x - 4) = 0 \]