The expression given is x²y³ + 11x²y + 6y² + 66. To find a factor, we can first try to factor this polynomial completely by grouping or using other factoring techniques.
1. Let’s rewrite the expression: we have terms with y raised to different powers and a constant at the end. So, we can organize it as:
- x²y³
- + 11x²y
- + 6y²
- + 66
2. Next, we can look for common factors in groups:
- Group 1: x²y³ + 11x²y
- Group 2: 6y² + 66
3. Factoring each group:
- In the first group (x²y³ + 11x²y), we can factor out x²y:
- x²y(y² + 11)
4. In the second group (6y² + 66), we can factor out 6:
5. Now, we rewrite the expression as:
x²y(y² + 11) + 6(y² + 11)
6. We see that we have a common factor of (y² + 11) in both groups:
(y² + 11)(x²y + 6)
In conclusion, one of the factors of the expression x²y³ + 11x²y + 6y² + 66 is (y² + 11).