What is a polynomial function?

Notes:

A polynomial function is a function in the form:

$f\left( x \right)\; = {a_n}{x^n} + \;{a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} +$…$+ {a_2}{x^2} + {a_1}x + {a_0}$

$\bullet$coefficients: ${a_n}$, ${a_{n - 1}}$, . . . , ${a_2}$, ${a_1}$
$\bullet$leading coefficient: "${a_n}$", the coefficient of the highest power of x
$\bullet$constant term: "${a_0}$", the term without $x$
$\bullet$degree of the polynomial function: $n$, the highest power of $x$