I'm reading Barbeau's polynomials, and he states:
For the polynomial $a_nt^n+a_{n-1}t^{n-1}+...+a_1t+a_0$, with $a_n \neq0 $, the numbers $a_i$ $(0 \leq i \leq n)$ are called coefficients.
Some pages later, there's a question:
Is $deg(p \circ q)$ related in any way to $deg(q \circ p)$?
Which I answered:
$deg(p\circ q)= deg(q\circ p)$ iff both polynomials have at least $a_1$, because we could have a constant polynomial in which I guess that the statement above would make no sense.
And then, when I went for the answer, I've found:
$deg$ $p\circ q$ $=$ $deg$ $q\circ p =(deg \, p)(deg \, q)$
So, considering two polynomials P and Q, both of $deg=0$, is it still possible to perform polynomial composition?