Find the zeros of the following quadratic polynomial: $p(x) = 3x^2 + 15x$. (in $, -5$)

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 $x^{3}-6 x^{2}+11 x-6$ by $x^{2}+x+1$.

Are the following statements 'True' or 'False'? Justify your answers.
The only value of $k$ for which the quadratic polynomial $k x^{2}+x+k$ has equal zeros is $\frac{1}{2}$.

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

The product of the zeros of a quadratic polynomial $p(x) = 3x^2 + 7x + 4$ is..........