To factor the quadratic expression \( x^2 + 4x - 21 \), we need to find two numbers that multiply to \(-21\) (the constant term) and add to \(4\) (the coefficient of the linear term).
The two numbers that work are \(7\) and \(-3\), since:
- \(7 \times -3 = -21\)
- \(7 + (-3) = 4\)
Now we can factor the expression:
\[ x^2 + 4x - 21 = (x + 7)(x - 3) \]
So, the factored form is \( (x + 7)(x - 3) \).
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