(x^4-13x^2+36) /(x-2)

(x^4-13x^2+36) /(x-2)

Let's factor the trinomial in the numerator

(x^2 - 9) (x^2 - 4) =

(x - 3)(x +3)(x- 2)(x +4)

So we have

[(x - 3)(x +3)(x- 2)(x +2)] / (x - 2)  =

[(x - 3) (x + 3) (x + 2)]

And no "long division" was necessary......