十字相乘法当系数a不等于1的时候该怎么分解,求教,(最好列举几个例子)

Question

十字相乘法当系数a不等于1的时候该怎么分解,求教,(最好列举几个例子)

Answer 1

分解因式,用十字相乘法,或者的确不方便,
我就是使用其他方法做草稿,
二次三项式,先把一次项一分为二,
这样分组分解,提公因式就方便了.
例如
6x" + 25x + 25
= 6x" + 15x + 10x + 25
= 3x( 2x + 5 ) + 5( 2x + 5 )
= ( 2x + 5 )( 3x + 5 )
6x" - 25x - 25
= 6x" - 30x + 5x - 25
= 6x( x - 5 ) + 5( x - 5 )
= ( x - 5 )( 6x + 5 )
2x" + 5x + 3
= 2x" + 2x + 3x + 3
= 2x( x + 1 ) + 3( x + 1 )
= ( x + 1 )( 2x + 3 )
3x" - 5x - 2
= 3x" - 6x + x - 2
= 3x( x - 2 ) + ( x - 2 )
= ( x - 2 )( 3x + 1 )
另一个方法,就是配方
4x" + 4x + 1
= ( 2x )" + 2( 2x ) + 1"
= ( 2x + 1 )"
像这样就有
2x" + 5x + 3
= ( 1/2 )( 4x" + 10x + 6 )
= ( 1/4 )( 1/2 )( 16x" + 40x + 24 )
= ( 1/8 )[ ( 4x )" + 10( 4x ) + 5" - 25 + 24 ]
= ( 1/8 )[ ( 4x + 5 )" - 1 ]
= ( 1/8 )[ ( 4x + 5 )" - 1" ]
= ( 1/8 )( 4x + 5 + 1 )( 4x + 5 - 1 )
= ( 1/2 )( 1/4 )( 4x + 6 )( 4x + 4 )
= ( 2x + 3 )( x + 1 )
还有
3x" - 5x - 2
= ( 1/3 )( 9x" - 15x - 6 )
= ( 1/4 )( 1/3 )( 36x" - 60x - 24 )
= ( 1/12 )[ ( 6x )" - 10( 6x ) + 5" - 25 - 24 ]
= ( 1/12 )[ ( 6x - 5 )" - 49 ]
= ( 1/12 )[ ( 6x - 5 )" - 7" ]
= ( 1/12 )( 6x - 5 - 7 )( 6x - 5 + 7 )
= ( 1/6 )( 1/2 )( 6x - 12 )( 6x + 2 )
= ( x - 2 )( 3x + 1 )
要么,也请你看看我的百度经验吧
希望你看过也觉得有用,对你也有所帮助.