Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=2 x^{3}+x^{2}-2 x-1$, $g(x)=x+1$.
Divide the polynomial $3 x^{4}-4 x^{3}-3 x-1$ by $x-1$.
Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x -1$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.