a) x3 - 6x2 + 11x - 6
= ( x3 - 2x2 ) - ( 4x2 - 8x ) + ( 3x - 6 )
= x2( x - 2 ) - 4x( x - 2 ) + 3( x - 2 )
= ( x - 2 )( x2 - 4x + 3 )
= ( x - 2 )( x2 - x - 3x + 3 )
= ( x - 2 )[ x( x - 1 ) - 3( x - 1 ) ]
= ( x - 2 )( x - 1 )( x - 3 )
b) x3 - 6x2 - 9x + 14
= ( x3 - x2 ) - ( 5x2 - 5x ) - ( 14x - 14 )
= x2( x - 1 ) - 5x( x - 1 ) - 14( x - 1 )
= ( x - 1 )( x2 - 5x - 14 )
= ( x - 1 )( x2 + 2x - 7x - 14 )
= ( x - 1 )[ x( x + 2 ) - 7( x + 2 ) ]
= ( x - 1 )( x + 2 )( x - 7 )
c) x3 + 6x2 + 11x + 6
= ( x3 + 2x2 ) + ( 4x2 + 8x ) + ( 3x + 6 )
= x2( x + 2 ) + 4x( x + 2 ) + 3( x + 2 )
= ( x + 2 )( x2 + 4x + 3 )
= ( x + 2 )( x2 + x + 3x + 3 )
= ( x + 2 )[ x( x + 1 ) + 3( x + 1 ) ]
= ( x + 2 )( x + 1 )( x + 3 )
e) x6 - 9x3 + 8
Đặt t = x3
bthuc <=> t2 - 9t + 8
= t2 - t - 8t + 8
= t( t - 1 ) - 8( t - 1 )
= ( t - 1 )( t - 8 )
= ( x3 - 1 )( x3 - 8 )
= ( x - 1 )( x2 + x + 1 )( x - 2 )( x2 + 2x + 4 )
