Decompose $X^{5}-2X^{4}+X^{3}-2X^{2}-2$ in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$

Question

Decompose $X^{5}-2X^{4}+X^{3}-2X^{2}-2$ in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$

So far i've tried to use Eisenstein which failed, and i tried to decompose this with modular groups. With mod(2) we succeeded then we can decompose this polynomial in:

$$X^{3}(X^{2}+1)$$

In mod3 i failed.

Please help, if i am doing this wrong tips/hints would be very appreciated

Kees