If one of the zeroes of the quadratic polynomial $(k-1) x^{2}+k x+1$ is $-3,$ then the value of $k$ is

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

The zero of $p(x) = x^{2} + 6x + 9$ is:

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 $x \in N$.

Divide $14x^3 - 5x^2 + 9x - 1$ by $2x - 1$.

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