Đặt: \(H=\)\(x^4-5x^3+7x^2-6\)
Giả sử: \(H=\left(x^2+ax+b\right)\left(x^2+cx+d\right)\)
\(=x^4+cx^3+dx^2+ax^3+acx^2+adx+bx^2+bcx+bd\)
\(=x^4+\left(a+c\right)x^3+\left(ac+b+d\right)x^2+\left(ad+bc\right)x+bd\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+c=-5\\ac+b+d=7\\ad+bc=0\\bd=-6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=-3\\b=3\\c=-2\\d=-2\end{matrix}\right.\)
\(\Rightarrow H=\left(x^2-3x+3\right)\left(x^2-2x-2\right)\)
ta có : \(x^4-5x^3+7x^2-6\)
\(=x^4-2x^3-2x^2-3x^3+6x^2+6x+3x^2-6x-6\)
\(=x^2\left(x^2-2x-2\right)-3x\left(x^2-2x-2\right)+3\left(x^2-2x-2\right)\)
\(=\left(x^2-3x+3\right)\left(x^2-2x-2\right)\)