Factorize the following polynomial: $p(x) = x^{3} - 4x^{2} + 5x - 20$.

For the given sum and product of zeroes,find a quadratic polynomial. Also,find the zeroes of this polynomial by factorisation:
Sum of zeroes = $\frac{-3}{2 \sqrt{5}}$,Product of zeroes = $-\frac{1}{2}$

In a prize-winning competition,$x+2$ students are qualified for the prize. If a total of $3x^3 + 10x^2 + 7x - 2$ prizes are distributed among them equally,find the number of prizes left undistributed,where $x \in N$.

Is the following statement True or False? Justify your answer. If the zeroes of a quadratic polynomial $ax^2 + bx + c$ are both negative,then $a, b,$ and $c$ all have the same sign.

Which of the following is a quadratic polynomial?

Obtain the value of the following polynomial at the given value of $x$: $p(x) = x^{4} + 2x^{3} - x + 2$; at $x = 2$.