Maximal ideal in the ring of polynomials over $\mathbb Z$ 
Let $\mathbb Z[x]$ the ring of polynomials with integers coefficients in one variable and $I =\langle 5,x^2 + 2\rangle$, how can I prove that $I$ is maximal ideal.

I tried first see that $5$ and $x^2+2$ are both polynomial in that ring but how can i get that is maximal ? some help please.

If you quotient by the ideal $I$, then 
$$5 \equiv 0 \pmod{I} \text{ and } x^2+2 \equiv 0 \pmod{I}.$$
This also suggests that $x^2 \equiv -2 \equiv 3 \pmod{I}$
This helps you get the idea that perhaps $x \mapsto \sqrt{3}$ and $5 \mapsto 0$
