Meaning of $\mathbb{Z}[X]$ set notation

Question

I'm confused with what the following means:

for a polynomial $h\in\mathbb{Z}[X]$ of positive degree.

In particular I'm unsure what the $\Bbb{Z}[X]$ bit means. The set of integers what? Thanks in advance

Answer 1

It is the set of the polynomials where the coefficients are integers. For example $h(X):=1-X\in\Bbb Z[X]$ but $g(X):=\sqrt2X+X^2\notin\Bbb Z[X]$

Answer 2

It is a ring, not just a set.

$$Z[X] = \{A_0 + A_1X + \dots + A_nX_n^n : A_n \in \mathbb{Z} \}$$