\(2x^3+x^2+x+2=0\)
\(\Rightarrow x^3+x^3+x^2+x+1+1=0\)
\(\Rightarrow\left(x^3+1\right)+\left(x^3+1\right)+\left(x^2+x\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x^2-x+1\right)+\left(x+1\right)\left(x^2-x+1\right)+x\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x^2-x+1+x^2-x+1+x\right)=0\)
\(\Rightarrow\left(x+1\right)\left(2x^2-x+2\right)=0\)
\(\Rightarrow x+1=0\Rightarrow x=-1\)
Vậy x = - 1 là nghiệm của đa thức \(2x^3+x^2+x+2=0\)