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

The sum of the zeros of a quadratic polynomial $p(x) = x^{2} + 3x + 2$ is ...........

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

State the degree of the given polynomial: $p(x) = 5x^{100} - (x^{10})^{20} + 3(x^2)^{25} + 2x^{25} - 7$

The total cost of $(x+1)$ cameras is ₹ $(x^{3}+3x^{2}+5x+3)$. Find the cost of one camera.

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 $(x \in N)$.