To solve the quadratic equation \( x^2 + 4x - 32 = 0 \) by factoring, we need to find two numbers that multiply to \(-32\) (the constant term) and add up to \(4\) (the coefficient of the \(x\) term).
The factors of \(-32\) that add up to \(4\) are \(8\) and \(-4\), because:
- \(8 \times -4 = -32\)
- \(8 + (-4) = 4\)
Thus, the factored form of the quadratic equation is: \[ (x + 8)(x - 4) = 0 \]
So, the correct response is: \((x+8)(x−4)=0\)