If $p(x) = 2x^4 - 3x^3 + 7x + 5$, then the value of $p(-2)$ is:

Answer the following and justify: What will be the quotient and remainder on division of $ax^{2} + bx + c$ by $px^{3} + qx^{2} + nx + s$,where $p \neq 0$?

What must be added to the polynomial $p(x) = 6x^5 + 5x^4 + 11x^3 - 3x^2 + x + 1$ so that the resulting polynomial is exactly divisible by $3x^2 - 2x + 4$? (Hint: add $-r(x)$ to $p(x)$)

Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder in each of the following:
$p(x) = x^{4} - 5x + 6, \quad g(x) = 2 - x^{2}$

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 3x^{2} - 6x + 8$,then $\alpha \beta \gamma = \dots$

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