To factor the quadratic equation \(x^2 - 8x - 20 = 0\), we need to find two numbers that multiply to \(-20\) (the constant term) and add up to \(-8\) (the coefficient of the x term).
The pairs of numbers that multiply to \(-20\) are:
- 1 and -20
- 2 and -10
- 4 and -5
Among these, we find that \(2\) and \(-10\) add up to \(-8\).
Thus, we can factor the quadratic as follows:
\[ x^2 - 8x - 20 = (x - 10)(x + 2) \]
Setting the factored expression to zero gives:
\((x - 10)(x + 2) = 0\)
So, the correct choice from the options provided is:
\((x - 10)(x + 2) = 0\)