Phân tích đa thức thành nhân tử: x^3-2x^2-8x
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a: \(x^4-2x^3+x^2-2x\)
\(=\left(x^4-2x^3\right)+\left(x^2-2x\right)\)
\(=x^3\left(x-2\right)+x\left(x-2\right)\)
\(=x\left(x-2\right)\left(x^2+1\right)\)
b: \(x^4+x^3-8x-8\)
\(=\left(x^4+x^3\right)-\left(8x+8\right)\)
\(=x^3\left(x+1\right)-8\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3-8\right)\)
\(=\left(x+1\right)\left(x-2\right)\left(x^2+2x+4\right)\)
\(8x^2-2x-3=8x^2+4x-6x-3=4x\left(2x+1\right)-3\left(2x+1\right)=\left(4x-3\right)\left(2x+1\right)\)
2x3 - x2 - 8x + 4 = x2(2x - 1) - 4(2x - 1) = (2x - 1)(x - 2)(x + 2)
2x3-x2 -8x+4=(2x3-x2)-(8x+4)
=x2(2x-1)-4(2x-1)
= (2x-1)(x2-4)
= (2x-1)(x-2)(x+2)
\(2x^3-5x^2+8x-3\)
\(\Leftrightarrow2x^3-x^2-4x^2+2x+6x+3\)
\(\Leftrightarrow x^2\cdot\left(2x-1\right)-2x\cdot\left(2x-1\right)+3\cdot\left(2x+1\right)\)
\(\Leftrightarrow\left(2x-1\right)\cdot\left(x^2-2x+3\right)\)
\(2x^3-5x^2+8x-3\)
\(=2x^3-x^2-4x^2+2x+6x-3\)
\(=x^2\left(2x-1\right)-2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x^2-2x+3\right)\)
= 2x^3 - 4x^2 - x^2 + 2x + 6x - 3
= 2x^2 ( x - 1/2 ) - x ( x - 1/2 ) +3 ( x - 1/2 )
= ( x - 1/2 )( 2x^2 - x + 3 )
x3 - 2x2 - 8x
= x( x2 - 2x - 8 )
= x( x2 - 4x + 2x - 8 )
= x[ x( x - 4 ) + 2( x - 4 ) ]
= x( x - 4 )( x + 2 )
\(x^3-2x^2-8x=x\left(x^2-2x-8\right)=x\left(x^2-2x+1-9\right)=x\left[\left(x-1\right)^2-3^2\right]=x\left(x-4\right)\left(x+2\right)\)