Question

M^3+6M^2+11m+6=0 find the factor

Answer 1

M³+6M²+11M+6=0
M³+M²+5M²+5M+6M+6=0
M²(M+1)+5M(M+1)+6(M+1)=0
(M+1){M²+5M+6}=0
(M+1){M²+2M+3M+6}=0
(M+1){M(M+2)+3(M+2)}=0
(M+1)(M+2)(M+3)=0


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Answer 2

Your question needs a correction :

Correct Question : m^3 + 6m^2 + 11m + 6 = 0

            Solution : -

⇒ m^3 + 6m^2 + 11m + 6 = 0

       Splitting 6m^2 in two terms

      6m^2 = 5m^2 + m^2

⇒ m^3 + m^2 + 5m^2 + 11m + 6 = 0

⇒ m^2( m + 1 ) + 5m^2 + 11m + 6 = 0

      Splitting 11m in two terms

      11m = 5m + 6m

⇒ m^2( m + 1 ) + 5m^2 + 5m + 6m + 6 = 0

⇒ m^2( m + 1 ) + 5m( m + 1 ) + 6( m + 1 ) = 0

⇒ ( m + 1 )( m^2 + 5m + 6 ) = 0

     Splitting 5m in two terms such that their product becomes 6

     5m = 2m + 3m

⇒ ( m + 1 ) { m^2 + 2m + 3m + 6 } = 0

⇒ ( m + 1 ) { m( m + 2 )  + 3( m + 2 ) } = 0

⇒ ( m + 1 ){ ( m + 2 ) ( m + 3 ) } = 0

⇒ ( m + 1 )( m + 2 )( m + 3 ) = 0

                 By Zero Product Rule : -

m = - 1

Or, m = -2

Or, m = - 3

( m + 1 ) , ( m + 2 ) and ( m + 3 ) are the factors of m^3 + 6m^2 + 11m + 6 = 0

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