Let $$p(x) = 2x^3+3x^2+4x+5.$$
As discussed in class, $p(2)$ can be computed via synthetic division by filling in for the letters $a$ through $g$ in the table $$\begin{array}{cccc} 2 & 3 & 4 & 5 \\ & b & d & f \\ a & c & e & g \\ \end{array}$$ where
$=a$,
$=b$,
$=c$,
$=d$,
$=e$,
$=f$,
$=g$.
Moreover, $p(2) =$ and $p(x)$ can be written as $$p(x) = (x-2)q(x) + r$$ where
$q(x) =$ is a quadratic polynomial and
$r=$ is a real number.