Evaluate the following using suitable identities : $(998)^{3}$

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

Expand each of the following, using suitable identities : $(x+2 y+4 z)^{2}$

Find the remainder obtained on dividing $p(x)=x^3+1$ by $x+1$.

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

$p(x)=2 x+1, \,\,x=\frac{1}{2}$

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

$p(x) = (x + 1) (x -2)$, $x = -\,1, \,2$