If $x-2$ is a factor of $x^{3}-3 x^{2}+a x+24$ then $a=\ldots \ldots \ldots$

From the following polynomials find out which of them has $(x+1)$ as a factor

$x^{3}+10 x^{2}+23 x+14$

By using the factor theorem, show that $(x-3)$ is a factor of the polynomial $12 x^{3}-31 x^{2}-18 x+9$ and then factorise $12 x^{3}-31 x^{2}-18 x+9$

Expand

$\left(\frac{x}{2}+\frac{2 y}{3}-\frac{3 z}{4}\right)^{2}$

Expand $:(3 x+7 y)(3 x-7 y)$