If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 6x^{2} - 7x$,then $\alpha + \beta + \gamma = \ldots$

Verify that $\frac{-2}{3}$ is a zero of the linear polynomial $p(x)=3x+2$.

Given that $x-\sqrt{5}$ is a factor of the cubic polynomial $x^{3}-3 \sqrt{5} x^{2}+13 x-3 \sqrt{5}$. Find all the zeroes of the polynomial.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$7 y^{2}-\frac{11}{3} y-\frac{2}{3}$

Find the division of the following by synthetic division method: $p(x) = x^{3} - 4x^{2} + 5x + 3$ by $x - 2$.

If $-2$ is a zero of the cubic polynomial $p(x) = x^3 + 6x^2 + 11x + 6$,then find the remaining zeros of $p(x)$.