Question

Phân tích các đa thức sau thành nhân tử:

a) (x-1)(2x+1)+3(x-1)(x+2)(2x+1)

b) (6x+3)-(2x-5)(2x+1)

c) (x-5)²+(x+5)(x-5)-(5-x)(2x+1)

d) (3x-2)(4x-3)-(2-3x)(x-1)-2(3x-2)(x+1)

Answer 1

a) ( x - 1 )( 2x + 1 ) + 3( x - 1 )( x + 2 )( 2x + 1 )

= ( x - 1 )( 2x + 1 )[ 1 + 3( x + 2 ) ]

= ( x - 1 )( 2x + 1 )( 1 + 3x + 6 )

= ( x - 1 )( 2x + 1 )( 3x + 7 )

b) ( 6x + 3 ) - ( 2x - 5 )( 2x + 1 )

= 3( 2x + 1 ) - ( 2x - 5 )( 2x + 1 )

= ( 2x + 1 )[ 3 - ( 2x - 5 ) ]

= ( 2x + 1 )( 3 - 2x + 5 )

= ( 2x + 1 )( 8 - 2x )

= 2( 2x + 1 )( 4 - x )

c) ( x - 5 )² + ( x + 5 )( x - 5 ) - ( 5 - x )( 2x + 1 )

= ( x - 5 )² + ( x + 5 )( x - 5 ) + ( x - 5 )( 2x + 1 )

= ( x - 5 )[ ( x - 5 ) + ( x + 5 ) + ( 2x + 1 ) ]

= ( x - 5 )( x - 5 + x + 5 + 2x + 1 )

= ( x - 5 )( 4x + 1 )

d) ( 3x - 2 )( 4x - 3 ) - ( 2 - 3x )( x - 1 ) - 2( 3x - 2 )( x + 1 )

= ( 3x - 2 )( 4x - 3 ) + ( 3x - 2 )( x - 1 ) - 2( 3x - 2 )( x + 1 )

= ( 3x - 2 )[ ( 4x - 3 ) + ( x - 1 ) - 2( x + 1 ) ]

= ( 3x - 2 )( 4x - 3 + x - 1 - 2x - 2 )

= ( 3x - 2 )( 3x - 6 )

= 3( 3x - 2 )( x - 2 )

Answer 2

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Answer 3

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