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\(x^4-3x^3-x+3\)
\(=x^4-x^3-2x^3+2x-3x+3\)
\(=\)\(x^3\left(x-1\right)-2x\left(x^2-1\right)-3\left(x-1\right)\)
\(=x^3\left(x-1\right)-2x\left(x-1\right)\left(x+1\right)-3\left(x-1\right)\)
\(=\left[x^3-2x\left(x+1\right)-3\right]\left(x-1\right)\)
\(=\left[x^3-2x^2-2x-3\right]\left(x-1\right)\)
\(=\)\(\left[x^3-3x^2+x^2-3x+x-3\right]\left(x-1\right)\)
\(=\left[x^2\left(x-3\right)+x\left(x-3\right)+\left(x-3\right)\right]\left(x-1\right)\)
\(=\left[\left(x-3\right)\left(x^2+x+1\right)\right]\left(x-1\right)\)
\(x^3-3x^2+6x-4\)
\(=x^3-2x^2+4x-x^2+2x-4\)
\(=\left(x^3-2x^2+4x\right)-\left(x^2-2x+4\right)\)
\(=x\left(x^2-2x+4\right)-\left(x^2-2x+4\right)\)
\(=\left(x-1\right)\left(x^2-2x+4\right)\)
x^3 - 3x^2 + 6x - 4
<=> x^3-3x^2+3x-1+3x-3
<=>(x-1)^3+3(x-1)
<=>(x-1)+((x-1)^2+3)
<=>(x-1)+(x^2-2x+4)
`a)3x-3a+yx-ya`
`=3(x-a)+y(x-a)`
`=(x-a)(y+3)`
`b)x^2-9-4(x+3)`
`=(x-3)(x+3)-4(x+3)`
`=(x+3)(x-3-4)`
`=(x+3)(x-7)`
a: \(=3\left(x^2-y^2-x+y\right)\)
\(=3\left[\left(x-y\right)\left(x+y\right)-\left(x-y\right)\right]\)
=3(x-y)(x+y-1)
b: =(x-4)(x+1)
c: =x(x-1)
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
=4x2-4=4(x2-1)=4(x-1)(x+1)
4(x2-1)