Are these rings a field?

Question

I want to check if the following rings are fiels:

1. $\mathbb{Z}[i]/\langle 5\rangle$
2. $\mathbb{Q}[x]/\langle x^2-2\rangle$
3. $\mathbb{F}_3[x]/\langle x^4+2\rangle$

For the first one I have found the ring homomorphism $\mathbb{Z}[i]\rightarrow \mathbb{Z}/5\times \mathbb{Z}/5$ with kernel $(5)\in \mathbb{Z}[i]$.

We conclude that this is not a field/, or not?