Factorize the following polynomial: $p(x) = x^{3} - 4x^{2} + 5x - 20$.

The degree of $p(x) = x^2(1 + x + x^2) + 5$ is.............

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 $(x \in N)$.

Answer the following and justify: If on division of a non-zero polynomial $p(x)$ by a polynomial $g(x)$,the remainder is zero,what is the relation between the degrees of $p(x)$ and $g(x)$?

Divide $x^{4}-5x+6$ by $2-x^{2}$.

Obtain the value of the following polynomial at the given value of $x$: $p(x) = 2x^4 - x^2 + 5x - 8$ at $x = -3$.