(x+5)(x+6)(x+10)(x+12)-2x^2 因式分解

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(x+5)(x+6)(x+10)(x+12)-2x^2 因式分解
(x+5)(x+6)(x+10)(x+12)-2x^2 因式分解

(x+5)(x+6)(x+10)(x+12)-2x^2 因式分解
( x + 5 )( x + 6 )( x + 10 )( x + 12 ) - 2x"
= ( x + 12 )( x + 5 )( x + 6 )( x + 10 ) - 2x"
= [ ( x" + 60 ) + 17x ][ ( x" + 60 ) + 16x ] - 2x"
= ( x" + 60 )" + ( 33x )( x" + 60 ) + 272x" - 2x"
下面开始分解
= ( x" + 60 )" + ( 18x )( x" + 60 ) + ( 15x )( x" + 60 ) + 270x"
= ( x" + 60 )( x" + 60 + 18x ) + ( 15x )( x" + 60 + 18 )
= ( x" + 15x + 60 )( x" + 18x + 60 )
分成两个因式,可能也行了,
在实数范围,还能继续分解
= ( x" + 15x + 60 )( x" + 18x + 9" - 81 + 60 )
= ( x" + 15x + 60 )[ ( x + 9 )" - 21 ]
= ( x" + 15x + 60 )( x + 9 + √21 )( x + 9 - √21 )
在复数范围,就能继续分成四个因式
= [ x" + 15x + (15/2)" - 225/4 + 240/4 ]( x + 9 + √21 )( x + 9 - √21 )
= [ ( x + 15/2 )" + 15/4 ]( x + 9 + √21 )( x + 9 - √21 )
= { x + 15/2 - [ (√15)/2 ]i }{ x + 15/2 + [ (√15)/2 ]i }( x + 9 + √21 )( x + 9 - √21 )

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