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 two numbers that satisfy these conditions are \(-10\) and \(2\) because:
\[ -10 \times 2 = -20 \] \[ -10 + 2 = -8 \]
Therefore, the factored form of the equation is:
\[ (x - 10)(x + 2) = 0 \]
So, the correct choice among the provided options is:
\(x - 10\) and \(x + 2 = 0\) (which corresponds to the choice \(x−10x+2=0\)).
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