Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$25 x ^ { 3 } y ^ { 4 } + 35 x ^ { 2 } y ^ { 5 } + 12 x y ^ { 6 }$$
A) $x y ^ { 4 } ( 5 x + 3 y ) ( 5 x + 4 y )$
B) $x \left( 5 x y ^ { 4 } + 3 y ^ { 5 } \right) ( 5 x + 4 y )$
C) $y ^ { 4 } ( 5 x + 3 y ) \left( 5 x ^ { 2 } + 4 x y \right)$
D) prime

Question

Quizplus · Accepted Answer

The polynomial can be factored by first factoring out the greatest common factor (GCF), which is $x y ^ { 4 }$, resulting in $x y ^ { 4 } ( 25 x ^ { 2 } + 35 x y + 12 y ^ { 2 })$. Then, by applying the grouping method to the trinomial inside the parentheses, we can factor it completely to get $x y ^ { 4 } ( 5 x + 3 y ) ( 5 x + 4 y )$.

Factor Completely Using the Grouping Method to Factor Trinomials 25x3y4+35x2y5+12xy625 x ^ { 3 } y ^ { 4 } + 35 x ^ { 2 } y ^ { 5 } + 12 x y ^ { 6 }25x3y4+35x2y5+12xy6

Factor Completely Using the Grouping Method to Factor Trinomials $25 x ^ { 3 } y ^ { 4 } + 35 x ^ { 2 } y ^ { 5 } + 12 x y ^ { 6 }$