Question

分解因式：x^3-7x+6=

Answer 1

x"' - 7x + 6

= x"' - x - 6x + 6

= x( x" - 1 ) - 6( x - 1 )

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

= ( x - 1 )( x" + x - 6 )

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

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

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

或者

= x"' - 1 - 7x + 6 + 1

= ( x"' - 1 ) - 7x + 7

= ( x - 1 )( x" + x + 1 ) - 7( x - 1 )

= ( x - 1 )( x" + x + 1 - 7 )

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

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

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