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1) \(x^6-x^4-9x^3+9x^2\)
\(=x^2\left(x^4-x^2-9x+9\right)\)
\(=x^2\left[x^2\left(x^2-1\right)-9\left(x-1\right)\right]\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
2) \(x^4-4x^3+8x^2-16x+16\)
\(=x^2\left(x^2+4\right)-4x\left(x^2+4\right)+4\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
3) \(x^4-25x^2+20x-4=x^4+5x^3-2x^2-5x^3-25x^2+10x+2x^2+10x-4\)
\(=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+5x-2\right)\left(x^2-5x+2\right)\)
4) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)\(=5x\left(x-2y\right)+2\left(x-2y\right)^2=\left(x-2y\right)\left(5x+2x-4y\right)=\left(x-2y\right)\left(7x-4y\right)\)
5) \(x^2\left(x^2-6\right)-x^2+9=x^4-7x^2+9\)
\(=x^4+x^3-3x^2-x^3-x^2+3x-3x^2-3x+9\)
\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-3\left(x^2+x-3\right)\)
\(=\left(x^2+x-3\right)\left(x^2-x-3\right)\)
6) \(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(y-4\right)^2+\left(y-4\right)^3=\left(y-4\right)^2\left(7x+y-4\right)\)
7) \(x^3+2x^2-6x-27=x^3-3x^2+5x^2-15x+9x-27\)
\(=x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2+5x+9\right)\)
\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)
\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)
\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)
b)3x^2-18x+27=3x^2-9x-9x+27=3x*(x-3)-9*(x-3)=(x-3)*(3x-9)=(x-3)*3*(x-3)=3*(x-3)^2
c)x^3-4x^2-12x+27=(x+3)*(x^2-3x+9-4)=(x+3)*(x^2-3x+5)
d)27x^3-1/27=(3x-1/3)*(9x^2-x+1/9) (hang dt)
con a) voi e) mk chiu
Ik mk nha, hôm nay ngày mai, ngày kia mk ik 3 lần lại cho bạn (thành 9 lần)
Nhớ kb với mìn lun nha!! Mk rất vui đc làm quen vs bạn, cảm ơn mn nhìu lắm
a) x3 - x2 - 5x + 125 = ( x\(^3\) + 125 ) - ( x\(^2\) + 5x ) = ( x + 5 ) ( x\(^2\) - 5x + 25 ) - x ( x + 5 )
= ( x + 5 ) ( x\(^2\) - 5x + 25 - x ) = ( x + 5 ) ( x\(^2\) - 6x + 25 )
b) x3 + 2x2 - 6x - 27 = ( x\(^3\) - 27 ) + ( 2x\(^2\) - 6x ) = ( x - 3 ) ( x\(^2\) + 3x + 9 ) + 2x ( x - 3 )
= ( x- 3 ) ( x\(^2\) + 3x + 9 + 2x ) = ( x - 3 ) ( x\(^2\) + 5x + 9 )
c) 12x3 + 4x2 - 27x - 9 = (12x3 + 4x2 ) - ( 27x + 9 ) = 4x\(^2\)( 3x + 1 ) - 9 ( 3x + 1 )
= ( 4x\(^2\) - 9 ) ( 3x -1 ) = ( 2x - 3 ) ( 2x + 3 ) ( 3x - 1 )
i) (x2 + 8x - 34)2 - (3x2 - 8x - 2)2
= (x2 + 8x - 34- 3x\(^2\) + 8x + 2) ( x\(^2\) + 8x - 34+3x2 - 8x - 2)
= ( -2x\(^2\) + 16x - 32 ) ( 4x\(^2\) - 36 )
= ( -2x\(^2\) + 16x - 32 ) ( 2x - 6 ) ( 2x + 6 )
a, x3- x2- 5x+ 125
=- (x2+ 5x)+ (x3+125)
=-x(x+5)+ (x+5)(x2- 5x+ 25)
=(x+5)(-x+x2- 5x+ 25)
=(x+ 5)(x2- 6x+ 25)