State the degree of the following polynomial: $p(x) = 6 - 5x^3 + 4x^5 - 5x^2$.

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

Are the following statements 'True' or 'False'? Justify your answers.
If all three zeroes of a cubic polynomial $x^{3}+ax^{2}-bx+c$ are positive,then at least one of $a, b$ and $c$ is non-negative.

Obtain the zeros of $p(x) = 6x^2 - x - 2$. Also,verify the relationship between the zeros and the coefficients of $p(x)$.

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

If $2x^3 - x^2 - 2x - 8$ is divided by $x - 2$,then the quotient polynomial is............