To factor the expression \( x^2 - 2x - 3 \), we need to find two numbers that multiply to \(-3\) (the constant term) and add to \(-2\) (the coefficient of the linear term).
The two numbers that satisfy these conditions are \(-3\) and \(1\), since:
\[ -3 \times 1 = -3 \quad \text{and} \quad -3 + 1 = -2 \]
Using these numbers, we can rewrite the expression as follows:
\[ x^2 - 2x - 3 = (x - 3)(x + 1) \]
Thus, the factored form of the expression \( x^2 - 2x - 3 \) is:
\[ (x - 3)(x + 1) \]
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