I done how to prove this the question is
A. Show that there is an automorphism of the ring of rational number $\mathbb{Q}(i)[x] $that has order of $4$.
I suppose i can say that if $\varphi$ is an automorphism, then $\varphi(x)=x$ for $x \in \mathbb{Q}$, and $\varphi(x)$ is a polynomial of degree one, say $mx+n$. If we consider what gets sent to $x$ by $\varphi$, we see that $m$ must be a unit of $\mathbb{Q}$, so $m=\pm 1$. I don't know I am right? If I am right how to continue to prove that it has order of $4$.
B. I have to show whether the following expression is reducible or not
$x^{42}+42x+4x^2+42$ over rational number $\mathbb{Q}$[x]
In this can I substitute any random rational numbers to prove that it is reducible or not?
A: Hint: Can you find an automorphism of $\mathbb{Q}(i)$ of order 4?
B: Consider using $p = 2$ with Eisenstein's criterion.