Divide the following by the synthetic division method: $p(x) = x^{3} - 3x^{2} - 3x + 1$ by $x + 1$.

(N/A) To divide $p(x) = x^{3} - 3x^{2} - 3x + 1$ by $x + 1$ using synthetic division:
$1$. Identify the coefficients of the dividend $p(x)$: $1, -3, -3, 1$.
$2$. Determine the root of the divisor $x + 1 = 0$,which gives $x = -1$.
$3$. Perform the synthetic division:
$\begin{array}{c|cccc} -1 & 1 & -3 & -3 & 1 \\ & & -1 & 4 & -1 \\ \hline & 1 & -4 & 1 & 0 \end{array}$
$4$. The bottom row represents the coefficients of the quotient and the remainder. The quotient is $q(x) = x^{2} - 4x + 1$ and the remainder is $r(x) = 0$.