Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+3 x^{3}+3 x^{2}+x+1$.

For $x+1=0,$ we have $x=-1$.

$\therefore $ The zero of $x+1$ is $-1$.

$\because$  $p ( x )= x ^{4}+3 x ^{3}+3 x ^{2}+ x +1$

$\therefore$  $p (-1)=(-1)^{4}+3(-1)^{3}+3(-1)^{2}+(-1)+1$

                             $=(1)+3(-1)+3(1)+(-1)+1 \div 1-3,+3-.1+1$

                              $=1 \neq 0$

            $\because$ $f (-1) \neq 0$

$\therefore$ $(x+1)$ is not a factor of $x^{4}+3 x^{3}+3 x^{2}+x+1$.