Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=3 x^{2}-1,\,x=-\,\frac{1}{\sqrt{3}},\, \frac{2}{\sqrt{3}}$
Factorise : $27 x^{3}+y^{3}+z^{3}-9 x y z$
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.
Find the value of the polynomial $5x -4x^2+ 3$ at $x = 2$.
Verify whether $2$ and $0$ are zeroes of the polynomial $x^{2}-2 x$.