1. ## Quick question about C[x]

Can we find irreducible polynomials in C[x] , C is the field of complex numbers,
other than f(x)= ax ? I wonder .

C is algebraically closed, so any polynomial has roots in C and hence can
be reduced to factors of lower degrees, except f(x)=x or in general f(x)=ax for
any constant a in C.

2. you're almost right. $f(x)=ax+b$ with $a,b \in \mathbb{C}, \ a \neq 0,$ are all irreducible elements of $\mathbb{C}[x].$

3. Thank you again!
BTW: I have some other questions posted here without any responses. I do really appreciate if you can help in one or more of them.