Final answer:
The greatest common factor for the set of terms 30x, 45x, 60x2, and 30x2 is 15x, identified by finding the largest common factor among the numerical coefficients and incorporating the variable with the lowest exponent.
Step-by-step explanation:
The greatest common factor (GCF) for the set of terms 30x, 45x, 60x2, and 30x2 can be found by identifying the common factors in the numerical coefficients and the variables of each term. To find the GCF of the numerical coefficients (30, 45, 60), we list their factors:
- 30: 1, 2, 3, 5, 6, 10, 15, 30
- 45: 1, 3, 5, 9, 15, 45
- 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors are 1, 3, 5, and 15, with 15 being the greatest. For the variables, since all terms have at least one 'x', the GCF will include 'x'. The term with the least power of 'x' is 'x' to the first power. Therefore, the GCF for all terms is 15x.