Final answer:
The factored form of the polynomial 6x²y³ - 15xyz + 4y is 3xy(2xy² - 5z + 4), which is option A.
Step-by-step explanation:
To factor the polynomial 6x²y³ - 15xyz + 4y, first identify the greatest common factor among all terms. Observing the given polynomial, we can see the greatest common factor is xyz. Therefore, we pull xyz out in front of the parentheses.
6x²y³ - 15xyz + 4y becomes xyz(6xy² - 15z + 4).
Checking if this common factor can be further simplified, we notice that the coefficients 6, -15, and 4 share a common factor of 3. Factoring this out gives us:
xyz(3(2xy² - 5z + 4/3)). The term 4/3 can't be in the parentheses since it must be an integer, hence we have the common factor as 3xy.
Thus, the factored form of the polynomial is 3xy(2xy² - 5z + 4), which corresponds to option A.