Hi, I need to show that $\displaystyle \alpha+1$=[x] is a primitive element of GF(9)= $\displaystyle \mathbb{Z}_3[x]/<x^{2}+x+2>$

I have already worked out that the function in the < > is irreducible but I do not know where to go from this.

there are 8 elements in the multiplicative group, what would they be? I guess it would be: 0, 2, x+2, what else? Im very unsure how to do this.

please help me would be appreciated thanks