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

When a polynomial $f(x)$ is divided by $x-3$ and $x+6,$ the respective remainders are $7$ and $22.$ What is the remainder when $f(x)$ is divided by $(x-3)(x+6)?$

If $a-b=1$ and $ab=6$,then what is the value of $(a^3-b^3)$?

Find the factors of $(a-b)^{3}+(b-c)^{3}+(c-a)^{3}$.

If $x=\sqrt{3}$,then the value of $x^{4}+2+\frac{1}{x^{4}}$ will be

If $x+y+z=0,$ what will be the value of $\frac{x^{2}+y^{2}+z^{2}}{x^{2}-y z} ?$