\(x^4-10x^3-15x^2+20x+4=0\)
\(\Leftrightarrow x^4-x^3-9x^3+9x^2-24x^2+24x-4x+4=0\)
\(\Leftrightarrow x^3\left(x-1\right)-9x^2\left(x-1\right)-24x\left(x-1\right)-4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-9x^2-24x-4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+2x^2-11x^2-22x-2x-4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x+2\right)-11x\left(x+2\right)-2\left(x+2\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2-11x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\\x^2-11x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)(x2 - 11x - 2 không có nghiệm hữu tỉ)
Vậy x = 1 hoặc x = -2.
