The value of $p(x) = 2x^{4} - 3x^{3} + 7x + 5$ at $x = -2$ is $\ldots \ldots \ldots \ldots$

State the degree of the following polynomial: $p(x) = 5x^8 - 6(x^2)^5 - 4x^3 - 14$.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0, a, b, c, d \in R)$ are $\alpha, \beta,$ and $\gamma$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

For the quadratic polynomial $p(x) = ax^2 + bx + c$; if $a = 6$,$b = 11$,and $c = 4$,then the quadratic polynomial 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 $(x \in N)$.