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# Solve the inequality -3x-2+-2x^2+x^4%0

### Videos

$x^{3}\left(1+x\right)+x^{2}\left(-x-1\right)+\left(-2-x\right)\left(1+x\right)\geq 0$

## Step-by-step explanation

Problem

${x^4-2x^2-3x-2}\geq {0}$
1

We can factor the polynomial $-2-3x-2x^2+x^4$ using synthetic division (Ruffini's rule). We search for a root in the factors of the constant term $-2$ and we found that $-1$ is a root of the polynomial

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

$x^{3}\left(1+x\right)+x^{2}\left(-x-1\right)+\left(-2-x\right)\left(1+x\right)\geq 0$