To factor the quadratic expression \( x^2 - x - 20 \), we are looking for two numbers that multiply to \(-20\) (the constant term) and add to \(-1\) (the coefficient of the \(x\) term).
The two numbers that fit these criteria are \(-5\) and \(4\), because:
- \(-5 \times 4 = -20\)
- \(-5 + 4 = -1\)
Now we can rewrite the expression using these numbers:
\[ x^2 - x - 20 = (x - 5)(x + 4) \]
Thus, the factored form of \( x^2 - x - 20 \) is:
\[ (x - 5)(x + 4) \]
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