lim _{x rightarrow-1} frac{x^{4}+2 x^{3}+x^{2}}{x+1}=

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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) = 0Step:4 ：(boxed{0})

Answer

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) = 0Step: 4 ：(boxed{0})

$\lim _{x \rightarrow-1} \frac{x^{4}+2 x^{3}+x^{2}}{x+1}=$

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