Final answer:
The polynomial 3xy-4x-9y+12 can be factored by grouping. By factoring out common factors from grouped terms, the polynomial can be written as (3y - 9y) - 4(x - 3) and ultimately factored into (x - 3)(3y - 4).
Step-by-step explanation:
To factor the polynomial by grouping, we need to rearrange the terms in a way that allows us to factor out common factors from each group. The polynomial given is 3xy-4x-9y+12. We can group the terms as follows: (3xy - 9y) + (-4x + 12). Now, let us factor out the common factors from each group.
From the first group (3xy - 9y), we can factor out a common factor of 3y, giving us 3y(x - 3). The second group (-4x + 12) has a common factor of 4, which can be factored out to get -4(x - 3).
Now we can write the original polynomial as 3y(x - 3) - 4(x - 3). We notice that (x - 3) is a common factor in both terms. Therefore, we can factor (x - 3) out, which gives us the final factored form of the polynomial: (x - 3)(3y - 4).