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

The zeros of $p(x) = 3x^2 - x - 4$ are $\alpha$ and $\beta$,then $\alpha^2 \beta + \alpha \beta^2 = \ldots$

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

Divide $x^{4}-3 x^{2}+4 x+5$ by $x^{2}-x+1$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$2s^{2} - (1 + 2\sqrt{2})s + \sqrt{2}$

Divide $x^{4}+4 x^{3}-2 x^{2}-12 x+9$ by $x^{2}-2 x+1$.