There are $x^{3}-3x^{2}+4x-4$ pens to be distributed in a class of $x-2$ students. Each student should get the maximum possible number of pens. Find the number of pens received by each student and the number of pens left undistributed $(x \in N)$.

(A) To find the number of pens received by each student and the remainder,we divide the polynomial $p(x) = x^{3}-3x^{2}+4x-4$ by the divisor $s(x) = x-2$ using synthetic division.
Setting the divisor $x-2 = 0$ gives $x = 2$.
Using synthetic division:
$\begin{array}{c|cccc} 2 & 1 & -3 & 4 & -4 \\ & & 2 & -2 & 4 \\ \hline & 1 & -1 & 2 & 0 \end{array}$
The quotient is $q(x) = x^{2}-x+2$ and the remainder is $0$.
Therefore,each student receives $x^{2}-x+2$ pens,and there are $0$ pens left undistributed.