x^3-14x+8 / x-4

First of all, what do you want to do ?

Secondly, you probably meant
(x^3-14x+8)/(x-4)
Thirdly, if your question had been
(x^3-14x-8)/(x-4)
then it would have divided out nicely, for a quotient of x^2 + 4x + 2

So what's up here?