Answer
$(a)$
$P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$
$a_n\ne0$
$(b)$
$P(c) = 0$
$c$ is a zero of function $P$ if $(x-c)$ is a factor of the function or if $c$ is an $x$-intercept of the graph of $P$.
Work Step by Step
$(a)$ The following expression is the general form of a polynomial function $P$ of degree $n$ :
$P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$
$a_n\ne0$
$(b)$
$c$ is a zero of $P$ means, that $P(c)=0$. Graphically, it is the point where the graph intercepts $x$-axis.
