To factor the quadratic expression \( x^2 - x - 12 \), we need to find two numbers that multiply to \(-12\) (the constant term) and add to \(-1\) (the coefficient of the linear term).
The two numbers that satisfy these conditions are \(-4\) and \(3\) because:
\[ -4 \times 3 = -12 \] \[ -4 + 3 = -1 \]
Now, we can factor the expression as follows:
\[ x^2 - x - 12 = (x - 4)(x + 3) \]
So the factored form of \( x^2 - x - 12 \) is:
\[ (x - 4)(x + 3) \]
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