Final answer:
The greatest common factor of 15x²y³ and −18x³yz is 3xy, which is obtained by factoring the coefficients and combining the smallest exponents of the variables present in both terms.
Step-by-step explanation:
To find the greatest common factor (GCF) of 15x²y³ and −18x³yz, we need to factor both expressions and find the largest factors they have in common. The coefficients 15 and 18 can be factored into prime factors, where 15 = 3 × 5 and 18 = 2 × 3².
We look at the variable components next. The variable 'x' appears in both terms, with the lowest exponent on 'x' being x². For the variable 'y', the lowest exponent is y in the second term, despite the first term having y³. Combining these common factors, the greatest common factor is found to be 3xy. Therefore, the correct answer is A. 3xy.