Evaluate using suitable identities : $(999)^{3}$

Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x$.

Write the coefficients of $x^2$ in each of the following : 

$(i)$ $\frac{\pi}{2} x^{2}+x$               $ (ii)$ $\sqrt{2} x-1$

Verify whether the following are zeroes of the polynomial, indicated against them.

$p(x)=5 x-\pi, \,\,x=\frac{4}{5}$

Find the zero of the polynomial : $p(x) = 3x$

Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.