phân tích đa thức thành nhân tử:\(x^3+7x-6\)
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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)`
x3 + 7x - 6
= x3 - x - 6x - 6
= x3 - x - 6 (x+1)
= x (x2 - 1) - 6 (x+1)
= (x + 1) ( x (x - 1) - 6 )
= ( x + 1) ((x2 - x - 6))
= (x + 1) ((x2 + 2 - 3 - 6))
= (x + 1) (x(x +2) - 3 ( x + 2))
= (x + 1)(x + 2)(x + 3)
\(x^3-7x-6\)
\(=x^3+2x^2-2x^2-4x-3x-6\)
\(=x^2\left(x+2\right)-2x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x+2\right)\left(x^2+x-3x-3\right)\)
\(=\left(x+2\right)\left[x\left(x+1\right)-3\left(x+1\right)\right]\)
\(=\left(x+2\right)\left(x+1\right)\left(x-3\right)\)
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)
\(x^3+7x-6=\left(x^3-1\right)+\left(7x-7\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)-7\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x-6\right)\)
\(=\left(x-1\right)\left(x^2+3x-2x-6\right)\)
\(=\left(x-1\right)\left(x+3\right)\left(x-2\right)\)
x3-7x+6=x3-x-6x+6=x(x-1)(x+1)-6(x-1)=(x-1)(x2+x-6)=(x-1)(x-2)(x+3)
\(x^3-7x+6=x^3+3x^2-3x^2-9x+2x+6\)
\(=x^2.\left(x+3\right)-3x.\left(x+3\right)+2.\left(x+3\right)\)
\(=\left(x+3\right).\left(x^2-3x+2\right)\)
\(=\left(x+3\right).\left(x^2-x-2x+2\right)\)
\(=\left(x+3\right).\left[x.\left(x-1\right)-2.\left(x-1\right)\right]\)
\(=\left(x+3\right).\left(x-1\right).\left(x-2\right)\)