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

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

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

If the zero of the polynomial $p(x) = 3x^{3} - x^{2} - ax - 45$ is $3$,then $a = \dots$

For each of the following,find a quadratic polynomial whose sum and product of the zeroes are as given respectively. Also,find the zeroes of these polynomials by factorisation.
Sum of zeroes $= -\frac{8}{3}$,Product of zeroes $= \frac{4}{3}$

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0)$ are $\alpha, \beta,$ and $\gamma,$ then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \dots$