Final answer:
The given expression is factored by taking out the greatest common factor of 8y², resulting in Option A: 8y²(3x + 5xy - 7y) as the correct factorization.
Correct option is Option A: 8y²(3x + 5xy - 7y).
Step-by-step explanation:
The question asks to factor the given expression 3472: 24xy² + 40x²y² - 56y³. To factor this expression by taking out the greatest common factor (GCF), we first identify the GCF of the coefficients (24, 40, 56) which is 8, and then we find the common variables in each term. The variable term y² is common to all, so it is also part of the GCF. Factoring out 8y² we get:
8y²(3x + 5x² - 7y)
Therefore, the factored form of the expression is Option A: 8y²(3x + 5xy - 7y).