Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.
Find the value of each of the following polynomials at the indicated value of variables : $p(t)=4 t^{4}+5 t^{3}-t^{2}+6$ at $t=a$.
Find the value of $k,$ if $x-1$ is a factor of $4 x^{3}+3 x^{2}-4 x+k$.
Factorise : $2 x^{2}+y^{2}+8 z^{2}-2 \sqrt{2} x y+4 \sqrt{2} y z-8 x z$
Factorise : $x^{3}+13 x^{2}+32 x+20$