Without actually calculating the cubes, find the value of :

$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$

With the help of the remainder theorem. examine whether $x+2$ is a factor of the polynomial $x^{3}+9 x^{2}+26 x+24$ or not.

Expand

$(x+4)(x+9)$

Factorise $: x^{3}+x^{2}-26 x+24$

Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by

$x+4$