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.

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

$(31)^{3}-(16)^{3}-(15)^{3}$

Classify the following as linear, quadratic or cubic polynomial

$x^{2}-9 x+14$

Factorise the following:

$9 x^{2}-12 x+3$

If $x+1$ is a factor of $a x^{3}+x^{2}-2 x+4 a-9,$ find the value of $a$.