To factor the quadratic equation \( x^2 + 4x - 32 = 0 \), we are looking for two numbers that multiply to \(-32\) (the constant term) and add to \(4\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(8\) and \(-4\), because:
- \(8 \times (-4) = -32\)
- \(8 + (-4) = 4\)
Thus, we can factor the quadratic equation as follows:
\[ x^2 + 4x - 32 = (x + 8)(x - 4) \]
So, the factored form of the quadratic equation \( x^2 + 4x - 32 = 0 \) is:
\[ (x + 8)(x - 4) = 0 \]