Question

4（x＋5）（x＋6）（x＋10）（x＋12）–3x^2 因式分解

Answer 1

4( x + 5 )( x + 6 )( x + 10 )( x + 12 ) - 3x"
= 4( x" + 17x + 60 )( x" + 16x + 60 ) - 3x"

= 4( x" + 16x + 60 + x )( x" + 16x + 60 ) - 3x"
= 4( x" + 16x + 60 )" + 4x( x" + 16x + 60 ) + x" - 4x"
= ( 2x" + 32x + 120 )" + 2x( 2x" + 32x + 120 ) + x" - 4x"
= ( 2x" + 32x + 120 + x )" - ( 2x )"
= ( 2x" + 33x + 120 + 2x )( 2x" + 33x + 120 - 2x )
= ( 2x" + 35x + 120 )( 2x" + 31x + 120 )

或者
= 4( x" + 17x + 60 )( x" + 17x + 60 - x ) - 3x"
= 4( x" + 17x + 60 )" - 4x( x" + 17x + 60 ) + x" - 4x"
= ( 2x" + 34x + 120 )" - 2x( 2x" + 34x + 120 ) + x" - 4x"
= ( 2x" + 34x + 120 - x )" - ( 2x )"
= ( 2x" + 33x + 120 + 2x )( 2x" + 33x + 120 - 2x )
= ( 2x" + 35x + 120 )( 2x" + 31x + 120 )