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Ta có `:`
`x^3 - 7x-6`
`= x^3 - 9x + 2x - 6`
`= x( x^2 - 9 ) + 2( x-3 )`
`= x( x-3 )( x + 3 ) + 2( x-3 )`
`= [ x( x + 3 )+2]( x-3 )`
`= ( x^2 + 3x + 2 )( x-3 )`
`= ( x^2 + 2x + x + 2 )( x-3 )`
`= [x( x+2 ) + ( x + 2 )]( x-3 )`
`= ( x+1)(x+2)(x-3)`
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3-7x-6\)
\(=x^3+2x^2-2x^2-4x-3x-6\)
\(=x^2\left(x+2\right)-2x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x+2\right)\left(x^2+x-3x-3\right)\)
\(=\left(x+2\right)\left[x\left(x+1\right)-3\left(x+1\right)\right]\)
\(=\left(x+2\right)\left(x+1\right)\left(x-3\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x³ -7x - 6
= x³ -x²+x²-x-6x- 6
= x²(x-1)+x(x-1)-6(x+1)
= (x-1)(x² +x) - 6(x+1)
= (x-1)x(x+1) - 6(x+1)
=(x2-x-6)(x+1)
=(x2 - 3x + 2x - 6)(x+1)
=[x(x+2)-3(x+2)](x+1)
=(x-3)(x+2)(x+1)
x³ -7x +6
= x³ -x²+x²-x-6x+6
= x²(x-1)+x(x-1)-6(x-1)
= (x-1)(x² +x-6)
= (x-1)(x²-2x+3x-6)
=(x-1)(x-2)(x+3)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
7x5( x - 1 ) - 3x2y6( 1 - x ) + 5xy3( x - 1 )
= 7x5( x - 1 ) + 3x2y6( x - 1 ) + 5xy3( x - 1 )
= x( x - 1 )[ 7x4 + 3xy6 + 5y3 )
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x3 - 7x - 6 = x3 + x2 - x2 - x - 6x - 6
= x2(x + 1) - x(x + 1) - 6(x + 1)
= (x + 1)(x2 - x - 6)
= (x + 1)(x2 + 2x - 3x - 6)
= (x + 1)[x(x + 2) - 3(x + 2)]
= (x + 1)(x + 2)(x - 3)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3-7x+6\)
\(=x^3-x^2-2x^2+2x+3x^2-3x-6x+6\)
\(=x^2\left(x-1\right)-2x\left(x-1\right)+3x\left(x-1\right)-6\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-2x+3x-6\right)\)
\(=\left(x-1\right)\left[\left(x^2-2x\right)+\left(3x-6\right)\right]\)
\(=\left(x-1\right)\left[\left(x-2\right)\left(x+3\right)\right]\)
\(=\left(x-1\right)\left(x-2\right)\left(x+3\right)\)
Ta có:x3-7x+6
=x3-x-6x+6
=x(x2-1)-6(x-1)
=x(x-1)(x+1)-6(x-1)
=(x2+x-6)(x-1)
\(x^3-7x-6=x^3-x-6x-6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x-6\right)=\left(x-1\right)\left(x^2+3x-2x-6\right)=\left(x-1\right)\left(x\left(x+3\right)-2\left(x+3\right)\right)\)
\(=\left(x-1\right)\left(x+3\right)\left(x-2\right)\)