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Sửa đề: x^3+6x^2+11x+6
=x^3+x^2+5x^2+5x+6x+6
=(x+1)(x^2+5x+6)
=(x+1)(x+2)(x+3)
\(=x^3-x+7x+7=x\left(x-1\right)\left(x+1\right)+7\left(x+1\right)\\ =\left(x+1\right)\left(x^2-x+7\right)\)
\(1,2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(2x+1\right)\left(x-2\right)\)
\(2,4x^2-7x-2\)
\(=4x^2-8x+x-2\)
\(=4x\left(x-2\right)+x-2\)
\(\left(4x+1\right)\left(x-2\right)\)
\(3x^2-11x+6\)
\(=3x^2-9x-2x+6\)
\(=\left(3x^2-9x\right)-\left(-2x+6\right)\)
\(=3x\cdot\left(x-3\right)-2\cdot\left(x-3\right)\)
\(=\left(3x-2\right)\cdot\left(x-3\right)\)
3x2 - 11x + 6
= 3x2 - 2x - 9x + 6
= ( 3x2 - 2x ) - ( 9x - 6 )
= x( 3x - 2 ) - 3( 3x - 2 )
= ( x - 3 )( 3x - 2 )
\(=\left(6x^2-3x\right)+\left(4x-2\right)\)
\(=3x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(3x+2\right)\left(2x-1\right)\)
\(=6x^2-3x+4x-2=6x\left(x-2\right)+2\left(x-2\right)=2\left(3x+2\right)\left(x-2\right)\)
\(6x^2-7x+2\)
\(=6x^2-3x-4x+2\)
\(=\left(6x^2-3x\right)-\left(4x-2\right)\)
\(=3x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(3x-2\right)\)
a) \(3x^2-6xy=3x\left(x-2y\right)\)
b) \(x^3-6x^2+9x=x\left(x^2-6x+9\right)=x\left(x-3\right)^2\)
c) \(=x\left(x-2y\right)-3\left(x-2y\right)=\left(x-2y\right)\left(x-3\right)\)
d) \(=2x\left(3x-5\right)-3\left(3x-5\right)=\left(3x-5\right)\left(2x-3\right)\)
\(a,=3x\left(x-2y\right)\\ b,=x\left(x-3\right)^2\\ c,Sửa:x^2-2xy-3x+6y=x\left(x-2y\right)-3\left(x-2y\right)=\left(x-2y\right)\left(x-3\right)\\ d,=\left(3x-5\right)\left(2x-3\right)\)
x3+6x2+11x+6 = x3+6x2+12x-x+8-2 = (x3+6x2+12x+8) - (x+2) = (x+2)3 - (x+2) = (x+2)[(x+2)2 - 1] = (x+2)(x+2-1)(x+2+1) = (x+2)(x+1)(x+3)