The zero of the linear polynomial $p(x) = ax + b$ is $\ldots \ldots \ldots \ldots$ $(a, b \neq 0)$.

Find the zeros of the following quadratic polynomial: $p(x) = 4x^2 - 256$.

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 $x \in N$.

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

If the sum of the zeros is $2$ and the product of the zeros is $3,$ then the quadratic polynomial is........

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