Step 1 :Factor the numerator: $x^{4}+2x^{3}+x^{2} = x^{2}(x+1)^{2}$
Step 2 :Cancel out the (x+1) term in both the numerator and the denominator: $\frac{x^{2}(x+1)^{2}}{x+1} = x^{2}(x+1)$
Step 3 :Evaluate the limit as x approaches -1: $\lim_{x \rightarrow -1} x^{2}(x+1) = 0$
Step 4 :\(\boxed{0}\)