Divide $x^{3}-3x^{2}-3x+1$ by $x+1$.

(N/A) To divide $x^{3}-3x^{2}-3x+1$ by $x+1$,we use polynomial long division:
$1$. Divide the first term of the dividend $(x^{3})$ by the first term of the divisor $(x)$ to get $x^{2}$.
$2$. Multiply $x^{2}$ by $(x+1)$ to get $x^{3}+x^{2}$. Subtract this from the dividend: $(x^{3}-3x^{2}-3x+1) - (x^{3}+x^{2}) = -4x^{2}-3x+1$.
$3$. Divide $-4x^{2}$ by $x$ to get $-4x$. Multiply $-4x$ by $(x+1)$ to get $-4x^{2}-4x$. Subtract this: $(-4x^{2}-3x+1) - (-4x^{2}-4x) = x+1$.
$4$. Divide $x$ by $x$ to get $1$. Multiply $1$ by $(x+1)$ to get $x+1$. Subtract this: $(x+1) - (x+1) = 0$.
Thus,the quotient is $x^{2}-4x+1$ and the remainder is $0$.