Question

Sophia was solving the following quadratic equation by factoring:
x2−8x−20=0. Which choice shows the correctly factored form of this equation?


x−5x−4=0

x−5x+4=0

x−10x−2=0

x−10x+2=0

Answer 1

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 \(x−10x+2=0\)).