Let $\mathbb{Z}[x]$ be the set of all polynomials in $x$ with integer coefficients.

Let $p,q\in \mathbb{Z}[x]$.

Identify which of the following binary operations are **not** closed on $\mathbb{Z}[x]$.

Let $deg(p)$ denote the degree $p$ and use the convention that degree of the zero polynomial is $-1$.