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

(NONE) According to the Factor Theorem,$(x + 1)$ is a factor of a polynomial $p(x)$ if and only if $p(-1) = 0$.
Let $p(x) = x^{4} + 3x^{3} + 3x^{2} + x + 1$.
Substitute $x = -1$ into the polynomial:
$p(-1) = (-1)^{4} + 3(-1)^{3} + 3(-1)^{2} + (-1) + 1$
$p(-1) = 1 + 3(-1) + 3(1) - 1 + 1$
$p(-1) = 1 - 3 + 3 - 1 + 1$
$p(-1) = 1$
Since $p(-1) = 1 \neq 0$,by the Factor Theorem,$(x + 1)$ is not a factor of the given polynomial.