\(x^2+3x+2=0\)
\(\Rightarrow x^2+2x+x+2=0\)
\(\Rightarrow x\left(x+1\right)+2\left(x+1\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-1\end{matrix}\right.\)
\(x^3-3x^2-x+3=0\)
\(\Rightarrow x^2\left(x-3\right)-\left(x-3\right)=0\)
\(\Rightarrow\left(x^2-1\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^2-1=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\pm1\\x=3\end{matrix}\right.\)
\(x^3+4x^2+5x^2=0\)
\(\Rightarrow x^3+9x^2=0\)
\(\Rightarrow x^2\left(x+9\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^2=0\\x+9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-9\end{matrix}\right.\)
