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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
e, \(x^3+5x^2+8x+4=x^3+x^2+4x^2+4x+4x+4\)
\(=x^2\left(x+1\right)+4x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
d, \(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
a) \(x^3+3x^2y-9xy^2+5y^3\)
\(=x^3-3x^2y+3xy^2-y^3+6x^2y-12xy^2+6y^3\)
\(=\left(x-y\right)^3+6y\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)^3+6y\left(x-y\right)^2\)
\(=\left(x-y\right)^2\left(x+5y\right)\)
b) \(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
c) \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
a) 27x3 - 27x2 + 18x - 4 ( sửa thành +18x nhé , chứ để như kia khó phân tích lắm :< )
= 27x3 - 18x2 - 9x2 + 12x + 6x - 4
= ( 27x3 - 18x2 + 12x ) - ( 9x2 - 6x + 4 )
= 3x( 9x2 - 6x + 4 ) - ( 9x2 - 6x + 4 )
= ( 9x2 - 6x + 4 )( 3x - 1 )
b) 2x3 - x2 + 5x + 3
= 2x3 - 2x2 + x2 + 6x - x + 3
= ( 2x3 - 2x2 + 6x ) + ( x2 -x + 3 )
= 2x( x2 - x + 3 ) + ( x2 - x + 3 )
= ( x2 - x + 3 )( 2x + 1 )
c) ( x2 - 3 )2 + 16
= x4 - 6x2 + 9 + 16
= x4 - 6x2 + 25
= x4 + 10x2 + 25 - 16x2
= ( x4 + 10x2 + 25 ) - 16x2
= ( x2 + 5 )2 - ( 4x )2
= ( x2 - 4x + 5 )( x2 + 4x + 5 )
a) \(12x^3+8x^2-3x-2=4x^2\left(3x+2\right)-\left(3x+2\right)\)
\(=\left(3x+2\right)\left(4x^2-1\right)=\left(3x+2\right)\left(2x-1\right)\left(2x+1\right)\)
b) \(18x^3+27x^2-2x-3=9x^2\left(2x+3\right)-\left(2x+3\right)\)
\(=\left(2x+3\right)\left(9x^2-1\right)=\left(2x+3\right)\left(3x-1\right)\left(3x+1\right)\)
c) \(8x^3+4x^2-34x+15=4x^2\left(2x-3\right)+8x\left(2x-3\right)-5\left(2x-3\right)\)
\(=\left(2x-3\right)\left(4x^2+8x-5\right)=\left(2x-3\right)\left(2x-1\right)\left(2x+5\right)\)
Mình viết xuôi theo dạng ax2 + bx + c nhé ;-; cho dễ làm
a) 2x2 + 7x + 3 = 2x2 + x + 6x + 3 = x( 2x + 1 ) + 3( 2x + 1 ) = ( 2x + 1 )( x + 3 )
b) 3x2 - 8x + 4 = 3x2 - 6x - 2x + 4 = 3x( x - 2 ) - 2( x - 2 ) = ( x - 2 )( 3x - 2 )
c) 3x2 - 7x + 2 = 3x2 - 6x - x + 2 = 3x( x - 2 ) - ( x - 2 ) = ( x - 2 )( 3x - 1 )
d) -6x2 + 7x - 2 = -6x2 + 3x + 4x - 2 = -3x( 2x - 1 ) + 2( 2x - 1 ) = ( 2x - 1 )( 2 - 3x )
e) -3x2 + 7x - 2 = -3x2 + 6x + x - 2 = -3x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 1 - 3x )
f) 2x2 - 5x + 2 = 2x2 - 4x - x + 2 = 2x( x - 2 ) - ( x - 2 ) = ( x - 2 )( 2x - 1 )
g) 3x2 - 8x + 4 = 3x2 - 6x - 2x + 4 = 3x( x - 2 ) - 2( x - 2 ) = ( x - 2 )( 3x - 2 )
h) 6x2 - 11x + 3 = 6x2 - 2x - 9x + 3 = 2x( 3x - 1 ) - 3( 3x - 1 ) = ( 3x - 1 )( 2x - 3 )
i) 2x2 + 3x - 27 = 2x2 - 6x + 9x - 27 = 2x( x - 3 ) + 9( x - 3 ) = ( x - 3 )( 2x + 9 )
j) 4x2 - 5x + 1 = 4x2 - 4x - x + 1 = 4x( x - 1 ) - ( x - 1 ) = ( x - 1 )( 4x - 1 )
\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)
\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)
\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)