Check whether $g(x)$ is a factor of $p(x)$ or not, where

$p(x)=8 x^{3}-6 x^{2}-4 x+3, \quad g(x)=\frac{x}{3}-\frac{1}{4}$

The following expressions are polynomials? Justify your answer:

$\frac{1}{5 x^{-2}}+5 x+7$

Expand

$\left(\frac{x}{2}+\frac{2 y}{3}-\frac{3 z}{4}\right)^{2}$

Without actually calculating the cubes, find the value of each of the following

$(14)^{3}+(27)^{3}-(41)^{3}$

Factorise the following:

$25 x^{2}+16 y^{2}+4 z^{2}-40 x y+16 y z-20 x z$