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

What are the possible expressions for the dimensions of a cuboid whose volume is given as $\left(2 x^{3}+15 x^{2}+33 x+20\right)$ cubic units? $(x>0)$

Factorise $: 4 x^{2}+4 x y-3 y^{2}$

Factorise the following quadratic polynomials by splitting the middle term

$12 x^{2}+23 x+5$

Expand

$(3 x+5)^{2}$