To factor the quadratic expression \( x^2 - 8x - 20 \), we want to find two numbers that multiply to \(-20\) (the constant term) and add up to \(-8\) (the coefficient of the linear term).
The two numbers that satisfy these conditions are \(-10\) and \(2\) because:
- \( -10 \times 2 = -20 \)
- \( -10 + 2 = -8 \)
Using these numbers, we can factor the expression as follows:
\[ x^2 - 8x - 20 = (x - 10)(x + 2) \]
So, the factored form of the quadratic expression \( x^2 - 8x - 20 \) is:
\[ (x - 10)(x + 2) \]