m3-4m2+m+6怎么因式分解.

Question

m3-4m2+m+6怎么因式分解.

Answer 1

m"' - 4m" + m + 6
分组分解
= m"' + 2m" + m - 6m" + 6
= m( m" + 2m + 1 ) - 6( m" - 1 )
= m( m + 1 )" - 6( m - 1 )( m + 1 )
提公因式,继续
= ( m + 1 )( m" + m - 6m + 6 )
= ( m + 1 )( m" - 5m + 6 )
= ( m + 1 )( m - 2 )( m - 3 )
或者
= m"' - 3m" - m" + m + 6
= m"( m - 3 ) - ( m" - m - 6 )
= m"( m - 3 ) - ( m" - 3m + 2m - 6 )
= m"( m - 3 ) - m( m - 3 ) - 2( m - 3 )
= ( m - 3 )( m" - m - 2 )
= ( m - 3 )( m - 2 )( m + 1 )
还有
= m'" - 4m" + 4m - 3m + 6
= m( m" - 4m + 4 ) - 3( m - 2 )
= m( m - 2 )" - 3( m - 2 )
= ( m - 2 )( m" - 2m - 3 )
= ( m - 2 )( m - 3 )( m + 1 )
分组分解的方式绝对不只一个,
关键就看你自己熟悉怎么样,
用一个方式做完,再用其他的检查一下.