To factor the quadratic expression \( x^2 - 6x - 7 \), we need to find two numbers that multiply to \(-7\) (the constant term) and add to \(-6\) (the coefficient of the \(x\) term).
The two numbers that satisfy these conditions are \(-7\) and \(1\) because:
\[ -7 \times 1 = -7 \] \[ -7 + 1 = -6 \]
Now we can write the factored form of the expression as:
\[ (x - 7)(x + 1) \]
So, the factored form of \( x^2 - 6x - 7 \) is:
\[ \boxed{(x - 7)(x + 1)} \]
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