Final answer:
The GCF of 45xy² and -60y is found by factoring both expressions, comparing the factors, and choosing the largest ones they have in common, which leads to the answer 15y.
Step-by-step explanation:
To find the greatest common factor (GCF) of 45xy² and -60y, we need to factor both expressions and then compare the factors to find the largest ones they have in common. First, let's factor the numbers and the variables.
- 45 = 3 × 3 × 5 = 3² × 5
- 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
- xy²: x × y × y
- y: y
Now, we compare the factors to find the common ones:
- The common numeric factors are 3 and 5, so we multiply them to get the common factor 15.
- For the variables, the common factor is y, since it is the only variable that appears in both expressions and we take the lowest power which is y.
Therefore, the GCF of 45xy² and -60y is 15y. The correct answer is option (a) 15y.