Properties of Degree

Theorem
Let $\struct {R, +, \circ}$ be a ring with unity whose zero is $0_R$.

Let $R \sqbrk X$ denote the ring of polynomial forms over $R$ in the indeterminate $X$.

For $f \in R \sqbrk X$ let $\map \deg f$ denote the degree of $f$.

Then the following hold: