Sophia was solving the following quadratic equation by factoring: x^2 -8x -20 = 0. Which choice shows the correctly factored form of this equation?

Question

A: (x-5) (x-4) = 0

B: (x-5) (x+4) = 0

C: (x-10) (x-2) = 0

D: (x -10) (x+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 to \(-8\) (the coefficient of \(x\)).

The pair of numbers that meets these criteria is \(-10\) and \(2\) since:

\[ -10 \times 2 = -20 \] \[ -10 + 2 = -8 \]

Thus, we can factor the equation as:

\[ (x - 10)(x + 2) = 0 \]

So, the correct choice from the options provided is:

D: (x - 10)(x + 2) = 0