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

$x-2$

By using the factor theorem, show that $(x+2)$ is a factor of the polynomial $6 x^{3}+19 x^{2}+16 x+4$ and then factorise $6 x^{3}+19 x^{2}+16 x+4$

Check whether $p(x)$ is a multiple of $g(x)$ or not :

$p(x)=x^{3}-5 x^{2}+4 x-3, \quad g(x)=x-2$

Factorise each of the following

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

Is $(x-1)$ is a factor of $3 x^{2}+7 x-10 ?$