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

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

Dividing $x^{3}+125$ by $(x-5),$ the remainder is $\ldots \ldots \ldots .$

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

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

If $x+2 a$ is a factor of $x^{5}-4 a^{2} x^{3}+2 x+2 a+3,$ find $a$

Factorise $: x^{3}-x^{2}-17 x-15$