Question

分解因式：x^4-5x^2+4=

Answer 1

x^4 - 5x" + 4
= (x" )" - x" - 4x" + 4
= x"( x" - 1 ) - 4( x" - 1 )
= ( x" - 1 )( x" - 4 )
= ( x - 1 )( x + 1 )( x - 2 )( x + 2 )
或者
= (x" )" - 4x" - x" + 4
= x"( x" - 4 ) - ( x" - 4 )
= ( x" - 4 )( x" - 1 )
= ( x - 2 )( x - 1 )( x + 1 )( x + 2 )

6x" + 7x - 6
= 6[ x" + (7/6)x + (7/12)" - (49/144) - 1 ]
= 6[ ( x + 7/12 )" - 193/144 ]
= 6[ x + 7/12 - (√193)/12 ][ x + 7/12 + (√193)/12 ]