$P(x) = 4x^{3} + 3x^{2} + 2x + 1$ is a $\ldots$ polynomial.

If the zero of the polynomial $p(x) = ax^2 - 11x + 3$ is $1$,then $a = \ldots$

For each of the following,find a quadratic polynomial whose sum and product of the zeroes are as given respectively. Also,find the zeroes of these polynomials by factorisation.
Sum of zeroes $= -\frac{8}{3}$,Product of zeroes $= \frac{4}{3}$

The number of real zeros of $y=p(x)$ is........... in the given figure.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$5 t^{2}+12 t+7$

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 $(x \in N)$.