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

question 21

Multiple Choice

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

---

Definitions:

Optimal Allocation

The most efficient distribution of resources within an economy to maximize the output or welfare.

MB = MC

A principle in economics indicating the optimal level of output or consumption, where the marginal benefit (MB) equals the marginal cost (MC).

Marginal Benefit

The added utility or pleasure that comes from the consumption of one more unit of a good or service.

Marginal Cost

The escalation in aggregate cost linked to the fabrication of an extra item of a good or service.