Identify the type of the given polynomial based on its degree: $p(x) = (x - 1)(2 - x)$

If one factor of $x^{3}+4 x^{2}+8 x+a$ is $(x+2)$,then find the value of $a$.

The maximum number of zeros of a polynomial having degree $k+1$ can be........

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

Find the division of the following by synthetic division method: $p(x) = x^{4} - a^{4}$ by $x - a$.

If the polynomial $p(x)$ is divided by $x^{2}+4x+2$, then the quotient polynomial $x^{2}-4x+14$ and the remainder polynomial $9x-13$ are obtained. Find the polynomial $p(x)$.