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 [tex]\frac{1}{(x+2)(x-4)}[/tex].
