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:
- \(8 \times (-4) = -32\)
- \(8 + (-4) = 4\)
Thus, we can express the quadratic equation in factored form as:
\[ (x + 8)(x - 4) = 0 \]
So, the factored form of the quadratic equation \(x^2 + 4x - 32 = 0\) is:
\[ (x + 8)(x - 4) = 0 \]
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