To determine which expressions are factors of the other terms given (6x³y, 6xy, 12x², 12, x², 1, and 2), we need to analyze each one.
1. **Factors of 6x³y**: This expression is divisible by:
- 6xy (it can be simplified by dividing by x² and y)
- 6xy is also a factor of itself.
- 12x² is not a factor because it requires dividing by y and the x exponent would not match.
- 12 is a factor only if you consider the coefficients (6 is a factor of 12).
- x² and 1 are factors since any term divisible by itself or 1 is a factor.
- 2 is also a factor as 6 includes 2 in its prime factorization.
2. **Factors of 6xy**: The same logic applies here:
- 6xy is a factor of itself.
- 12x² does not fit as a factor.
- 12 is a factor of 6xy under evaluation.
- x² and 1 remain factors.
- 2 is also a valid factor.
3. **Factors of 12x²**: From here, the factors become clearer. This term includes:
- 12 is a factor of itself.
- But it would also include 6x, 6, x, and 1.
- 2 is also still valid as we’ve evaluated previously.
Overall, when considering the original expressions, the following are confirmed as factors:
- x²
- 1
- 2
- 6xy (to a lesser degree)
- 12 (contextual for coefficients)
Thus, depending on the context of factors and equations, multiple expressions can serve as factors.