Consider the ring $\mathbb{R}[x]$. Then which of the following quotients is an integral domain?

Question

Which of the following quotient rings is an integral domain:

1. $\mathbb{R}[x]/(x^2+x+1)$
2. $\mathbb{R}[x]/(x^2+5x+6)$
3. $\mathbb{R}[x]/(x^3-2)$
4. $\mathbb{R}[x]/(x^7+1)$

Now we know that $R/(a)$ is an ID iff $(a)$ is a prime ideal. Here $x^2+5x+6=(x+3)(x+2)$ so $(x^2+5x+6)$ cannot be prime ideal, hence option $2$ is wrong. But I am confused with rest of the options. All the polynomials are primitive. Does this observation provides any help? How should I proceed? Please help.