To determine which expression is a factor of the polynomial 3xy + 2x + 18y + 12, we can look for common factors in each term.
First, let’s rearrange the polynomial a bit for clarity:
(3xy + 18y) + (2x + 12)
In the first group (3xy + 18y), we can factor out 3y:
3y(x + 6)
In the second group (2x + 12), we can factor out 2:
2(x + 6)
So, we can rewrite the expression as:
3y(x + 6) + 2(x + 6)
Now, we can factor out the common term (x + 6):
(x + 6)(3y + 2)
This shows that one of the factors of the original expression is (x + 6). Therefore, (x + 6) is indeed a factor of 3xy + 2x + 18y + 12.