Factor the GCF: 12x3y + 6x2y2 - 9xy3.

3x2y (4x2 + 2xy - 3)

3xy (4x + 2xy - 3y2)

3xy (4x2 + 2xy - 3y2)

3x2y (4x3y - 2x2y2 - 3xy3)

To answer the problem above, determine the GCF of the terms. For the numerical coefficients 12, 6, and 9, the GCF is 3. For the x^3, x^2, and x the GCF is x. Lastly, for y, y^2 and y^3, the GCF is y. Thus, the GCF of the terms is 3xy. Divide each of the terms with the GCF. The division will lead to the factors:

3xy (4x^2 + 2xy - 3y^2)

Thus the answer is the third choice.