Establish, whether or not following subsets of given rings are subrings
- All polynomials $f(x)$ with $f(0)=9$ in $\mathbb{Z}[x]$.
These are past paper questions, I have no clue what $\mathbb{Z}[x]$ is, can anyone give me some help please. There are also two more questions:
Establish, whether or not following subsets of given rings are ideals:
All integers divisible by $5$ in $\mathbb{Q}$ ($\mathbb{Q}$ is the field of rational numbers).
All polynomials in $\mathbb{Z}[x]$ with coefficients divisible by $5$ in $\mathbb{Z}[x]$.
Thank you so much