Factorise
$x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x$
The following expressions are polynomials? Justify your answer:
$\sqrt{3} x^{2}-2 x$
Factorise :
$x^{3}+x^{2}-4 x-4$
Factorise
$x^{2}+9 y^{2}+4+6 x y+12 y+4 x$
If the polynomial $a x^{3}+4 x^{2}+3 x-4$ and polynomial $x^{3}-4 x+a$ leave the same remainder when each is divided by $x-3,$ find the value of $a$.