Yes/No Is $\frac{ \mathbb{Q}[x] }{<x+2>}$ is Field?

Question

Is $\frac{ \mathbb{Q}[x] }{<x+2>}$ is Field ?

My attempt : I don't think it is field because $ x+2$ is reducible in $\mathbb{Q[x]}$ and for field $ x+2$ must be irreducible in $\mathbb{Q[x]}$

Is its true ?

Answer 1

How is $\;x+2\;$ reducible in $\;\Bbb Q[x]\;$ ...or even in $\;\Bbb R[x]\;,\;\;\Bbb C[x]\;$ ? It is a linear polynomial and it is thus irreducible, which makes the ideal $\;\langle x+2\rangle\;$ prime and thus maximal (why?), and thus $\;\Bbb Q[x]/\langle x+2\rangle\;$ is a field.

Be sure you can follow and understand all the above, and try now to answer: to what very well known field is the quotient isomorphic?