Final answer:
The correct factorization of the polynomial 3xy + 12xy is 3xy(1 + 4y), which corresponds to choice a) in the question provided.
Step-by-step explanation:
To factor the polynomial completely, we need to find the greatest common factor (GCF) of the terms in the polynomial 3xy' + 12xy. We can observe that both terms have a common factor of 3xy. Therefore, we can factor out 3xy from each term to get the completely factored form:
3xy(y') + 3xy(4) = 3xy(y' + 4).
However, since the original problem might have contained a typo with 'y'', we will assume it was intended to be 'y' and rewrite the polynomial as 3xy + 12xy. Factoring out the common factor 3xy, we get:
3xy(1) + 3xy(4) = 3xy(1 + 4) = 3xy(1 + 4y) after restoring the correct term.
Therefore, choice a) 3xy(x + 4y) is the correct factorization of the given polynomial.