Sophia was solving the following quadratic equation by factoring:

x^2 - 8x - 20 = 0. Which choice shows the correctly factored form of this equation?
a (x-5)(x-4)=0
b (x-5)(x+4)=0
c (x-10)(x-2)=0
d (x-10)(x+2)=0

1 answer

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 numbers that satisfy these conditions are \(-10\) and \(2\) because:

  • \(-10 \times 2 = -20\)
  • \(-10 + 2 = -8\)

Therefore, we can express the equation in its factored form as: \[ (x - 10)(x + 2) = 0 \]

Thus, the correct choice is: d (x-10)(x+2)=0.