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

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$t^{3}-2 t^{2}-15 t$

Identify the type of the following polynomial based on its degree: $p(x) = (x - 15)(x + 15)$

Answer the following and justify: If on division of a non-zero polynomial $p(x)$ by a polynomial $g(x)$,the remainder is zero,what is the relation between the degrees of $p(x)$ and $g(x)$?

Are the following statements 'True' or 'False'? Justify your answers.
If the zeroes of a quadratic polynomial $ax^2 + bx + c$ are both positive,then $a, b$ and $c$ all have the same sign.

Find the division of the following by synthetic division method: $p(x) = x^{3} - 2x^{2} + x - 2$ by $x + 1$.