Factorise the following:
$9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z$

Using the remainder theorem,find the remainder when the polynomial $p(x) = x^3 + x^2 - 26x + 24$ is divided by the divisor $x + 1$.

On dividing $p(x) = x^{3} + 2x^{2} - 5ax - 7$ by $(x + 1)$,the remainder is $R_{1}$ and on dividing $q(x) = x^{3} + ax^{2} - 12x + 6$ by $(x - 2)$,the remainder is $R_{2}$. If $2R_{1} + R_{2} = 6$,then find the value of $a$.

Write the coefficient of $x^{2}$ in the following polynomial: $x^{3} + 27$.

State whether the following statement is true or false:
$x^{2}-8x+12 = (x-6)(x-2)$

Using the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 6$.