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

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

Find the quotient and the remainder when $2 x^{2}-7 x-15$ is divided by

$x-2$

By remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where

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

Factorise each of the following

$x^{3}-125 y^{3}-15 x^{2} y+75 x y^{2}$

Without finding the cubes, factorise $(x-y)^{3}+(y-z)^{3}+(z-x)^{3} .$