How to factorized this 4th degree polynomial? I need your help to this polynomial's factorization.
Factorize this polynomials which doesn't have roots in Q. 
$ \ f(x) = x^4 +2x^3-8x^2-6x-1 $ 
P.S.) Are there any generalized method finding 4th degree polynomials factor?

You can always find the roots of a fourth degree polynomial. The formulas are not pretty, but they do exist.
Using the formulas, or, like me, using Wolfram Alpha, can show you that the roots of the polynomial are $1\pm\sqrt{2}$ and $-2\pm \sqrt{3}$ so the polynomial is
$$\begin{align}f(x)&=(x-1-\sqrt{2})(x-1+\sqrt{2})(x+2-\sqrt{3})(x+2+\sqrt{3})\\&=(x^2-2x-1)(x^2+4x+1)\end{align}$$
