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

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