Properties of Degree

Theorem
Let $(R, +, \circ)$ be a ring with unity whose zero is $0_R$.

Let $R \left[{X}\right]$ be the ring of polynomial forms over $R$ in the indeterminate $X$.

For $f \in R \left[{X}\right]$ let $\deg(f)$ be the degree of $f$.

Then the following hold: