Factor the expression below completely, if possible $18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }$
A) $3 m n ( m - 2 n ) ( 6 m - 7 n )$
B) $3 m n ( m + 2 n ) ( 6 m + 7 n )$
C) $3 m n ( m - 2 n ) ( 6 m + 7 n )$
D) $3 m n ( m + 2 n ) ( 6 m - 7 n )$
E)The expression is prime.

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor, which is $3mn$, resulting in $3mn(6m^2 - 19mn + 14n^2)$. Factoring the trinomial inside the parentheses gives $3mn(m-2n)(6m-7n)$.

Factor the Expression Below Completely, If Possible 18m3n−57m2n2+42mn318 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }18m3n−57m2n2+42mn3

Factor the Expression Below Completely, If Possible $18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }$