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

Which of the following statements is true?

In a prize-winning competition,$x+2$ students are qualified for the prize. If a total of $3x^3 + 10x^2 + 7x - 2$ prizes are distributed among them equally,find the number of prizes left undistributed,where $x \in N$.

If the product of the zeros of $p(x) = ax^{2} - 6x - 6$ is $4$,then $a = $ ............

Divide $x^{4}+2x^{3}+3x^{2}+2x+20$ by $x^{2}+2x+2$.

Find the zeros of the following quadratic polynomial: $5x^2 + 8x + 3$.