It's clear that a polynomial has a "degree". For instance our $$x^2 + 2x + 3$$ is a of degree two.
Can we apply the "degree" terminology to the coefficients? Here we have the coefficient tuple $[1\ 2\ 3]$. Can we call $2$ the "degree one coefficient" by synecdoche (meaning it's the coefficient of the degree one term of the polynomial)?
If not, how else do we pinpoint a particular coefficient position? In particular, without depending on the order of the syntax?
Even if the formula is given non-canonically as $2x + 3 + x^2$, how can we fill in "the ___ coefficient" in a way which unambiguously refers to the $2$?