# Step-by-step Solution

## Find the limit of $\frac{x^4+2x^3+x^2}{x+1}$ as $x$ approaches $-1$

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to{\left(-1\right)}}\left(\frac{x^4+2x^3+x^2}{x+1}\right)$
1

We can factor the polynomial $x^4+2x^3+x^2$ using synthetic division (Ruffini's rule). We found that $-1$ is a root of the polynomial

${\left(-1\right)}^4+2\left({\left(-1\right)}^3\right)+{\left(-1\right)}^2=0$

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$\lim_{x\to{\left(-1\right)}}\left(\frac{x^4+2x^3+x^2}{x+1}\right)$

Limits

~ 0.05 seconds