十字相乘法分解因式

十字相乘法分解因式
十字相乘法分解因式

十字相乘法分解因式
( x" - 3 )" - 4x"
= ( x" - 3 )" - ( 2x )"
= ( x" - 2x - 3 )( x" + 2x - 3 )
= ( x" + x - 3x - 3 )( x" - x + 3x - 3 )
= [ x( x + 1 ) - 3( x + 1 ) ][ x( x - 1 ) + 3( x - 1 ) ]
= ( x + 1 )( x - 3 )( x + 3 )( x - 1 )
= ( x - 1 )( x + 1 )( x - 3 )( x + 3 )

( 3x" + 2x + 1 )" - ( 2x" + 3x + 3 )"
= ( 3x" + 2x + 1 + 2x" + 3x + 3 )( 3x" + 2x + 1 - 2x" - 3x - 3 )
= ( 5x" + 5x + 4 )( x" - x - 2 )
= ( 5x" + 5x + 4 )( x" + x - 2x - 2 )
= ( 5x" + 5x + 4 )[ x( x + 1 ) - 2( x + 1 ) ]
= ( 5x" + 5x + 4 )( x + 1 )( x - 2 )

( a" + 8a )" + 22( a" + 8a ) + 120
= ( a" + 8a )" + 12( a" + 8a ) + 10( a" + 8a ) + 120
= ( a" + 8a )( a" + 8a + 12 ) + 10( a" + 8a + 12 )
= ( a" + 8a + 10 )( a" + 2a + 6a + 12 )
= ( a" + 8a + 10 )[ a( a + 2 ) + 6( a + 2 ) ]
= ( a" + 8a + 10 )( a + 2 )( a + 6 )
如果扩大到实数范围
= ( a + 2 )( a + 6 )( a" + 8a + 4" - 16 + 10 )
= ( a + 2 )( a + 6 )[ ( a + 4 )" - 6 ]
= ( a + 2 )( a + 6 )( a + 4 + √6 )( a + 4 - √6 )

( x" + 2x - 3 )( x" + 2x - 24 ) + 90
= ( x" + 2x )" - 27( x" + 2x ) + 72 + 90
= ( x" + 2x )" - 18( x" + 2x ) - 9( x" + 2x ) + 162
= ( x" + 2x )( x" + 2x - 18 ) - 9( x" + 2x - 18 )
= ( x" + 2x - 9 )( x" + 2x - 18 )
如果扩大到实数范围
= ( x" + 2x + 1 - 10 )( x" + 2x + 1 - 19 )
= ( x + 1 + √10 )( x + 1 - √10 )( x + 1 + √19 )( x + 1 - √19 )

( x" + x )" - 17( x" + x ) + 60
= ( x" + x )" - 12( x" + x ) - 5( x" + x ) + 60
= ( x" + x )( x" + x - 12 ) - 5( x" + x + 12 )
= ( x" + x - 5 )( x" + 4x - 3x - 12 )
= ( x" + x - 5 )[ x( x + 4 ) - 3( x + 4 ) ]
= ( x" + x - 5 )( x - 3 )( x + 4 )
如果扩大到实数范围
= ( x - 3 )( x + 4 )( 4x" + 4x + 1 - 1 - 20 ) / 4
= ( 1/4 )( x - 3 )( x + 4 )[ ( 2x + 1 )" - 21 ]
= ( 1/4 )( x - 3 )( x + 4 )( 2x + 1 + √21 )( 2x + 1 - √21 )

( x" + 2x )" - 7( x" + 2x ) - 8
= ( x" + 2x )" + ( x" + 2x ) - 8( x" + 2x ) - 8
= ( x" + 2x )( x" + 2x + 1 ) - 8( x" + 2x + 1 )
= ( x" + 2x + 1 )( x" + 2x - 8 )
= ( x + 1 )"( x" - 2x + 4x - 8 )
= ( x + 1 )"[ x( x - 2 ) + 4( x - 2 ) ]
= ( x + 1 )"( x - 2 )( x + 4 )

x"( x - 2 )" - 9
= ( x" - 2x )" - 3"
= ( x" - 2x + 3 )( x" - 2x - 3 )
= ( x" - 2x + 3 )( x" - 3x + x - 3 )
= ( x" - 2x + 3 )[ x( x - 3 ) + ( x - 3 ) ]
= ( x" - 2x + 3 )( x - 3 )( x + 1 )

( 3x" + 2x + 1 )" - ( 2x" + 3x + 3 )"
= ( 3x" + 2x + 1 + 2x" + 3x + 3 )( 3x" + 2x + 1 - 2x" - 3x - 3 )
= ( 5x" + 5x + 4 )( x" - x - 2 )
= ( 5x" + 5x + 4 )( x" + x - 2x - 2 )
= ( 5x" + 5x + 4 )[ x( x + 1 ) - 2( x + 1 ) ]
= ( 5x" + 5x + 4 )( x + 1 )( x - 2 )