\(x^3-7x+6=0\\ \Leftrightarrow x^3-x^2+x^2-x-6x+6=0\\ \Leftrightarrow x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)=0\\ \Leftrightarrow\left(x^2+x-6\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x^2-2x+3x-6\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x\left(x-2\right)+3\left(x-2\right)\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+3\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\\x=1\end{matrix}\right.\)
\(x^4-4x^3+12x-9=0\\ \Leftrightarrow x^4-4x^3+3x^2-3x^2+12x-9=0\\ \Leftrightarrow x^2\left(x^2-4x+3\right)-3\left(x^2-4x+3\right)=0\\ \Leftrightarrow\left(x^2-4x+3\right)\left(x^2-3\right)=0\\ \Leftrightarrow\left(x^2-3x-x+3\right)\left(x^2-3\right)=0\\ \Leftrightarrow\left(x\left(x-3\right)-\left(x-3\right)\right)\left(x^2-3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x-1\right)\left(x^2-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\\x=\pm\sqrt{3}\end{matrix}\right.\)
\(x^5-5x^3+4x=0\\ \Leftrightarrow x^5-x^3-4x^3+4x=0\\ \Leftrightarrow x^3\left(x^2-1\right)-4x\left(x^2-1\right)=0\\ \Leftrightarrow\left(x^3-4x\right)\left(x^2-1\right)=0\\ \Leftrightarrow x\left(x^2-4\right)\left(x-1\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm2\\x=\pm1\end{matrix}\right.\)
\(x^4-4x^3+3x^2+4x-4=0\\ \Leftrightarrow x^4-4x^3+4x^2-x^2+4x-4=0\\ \Leftrightarrow x^2\left(x^2-4x+4\right)-\left(x^2-4x+4\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x^2-4x+4\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)^2=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\\x=2\end{matrix}\right.\)
