Which of the following is the reciprocal of the factored form of: x2 - 2x - 8

We are given quadratic x^2-2x-8.

Let us factor it by product sum rule.

According to product sum rule, we need to find the factors of -8 that add upto -2.

If we write all factors of 8, we get 8,4,2 and 1 factores.

So, we could choose -4 and +2.

Because -4+2 = -2 (sum) and -4*2=-8 (product)

x^2-2x-8

Splitting middle term into two terms -4x+2x

x^2-4x+2x−8

Factoring out gcf from each group.

x(x-4) +2(x- 4)

(x + 2)(x - 4)

So, we got factored form of the given euadratic (x + 2)(x - 4).

Reciprocal of it would be .