Final answer:
The expression 3x³y² - 2x²y + 5xy has a greatest common factor of xy, leading to the factored form xy(3x²y - 2x + 5). None of the provided answer choices match this correct factored form, indicating a possible typo or mistake in the question or answer choices.
Step-by-step explanation:
To factor the expression using the greatest common factor (GCF) of 3x³y² - 2x²y + 5xy, first we need to identify the GCF. Each term has at least one x and one y.
The smallest powers of x and y in the expression are, respectively, 1 and 1. Thus, the GCF is xy. Now divide each term by xy to find the remaining factors:
- (3x³y²) / (xy) = 3x²y
- (-2x²y) / (xy) = -2x
- (5xy) / (xy) = 5
Now we write the expression as the product of the GCF and the remaining factors:
xy(3x²y - 2x + 5)
However, the expression within parentheses does not match any of the options provided in the question.
Since none of the listed answer choices is correct, the best course of action is to inform the student of the discrepancy and present the accurate factoring above. It seems there may have been a typo or mistake in the question or answer choices given.