Understanding the Expression
To determine which expression is a factor of 3xy + 2x + 18y + 12, we first need to simplify and analyze the terms of the provided expression. The expression can be rearranged to facilitate factoring.
Rearranging the Expression
The expression can be grouped as follows:
3xy + 18y + 2x + 12
Now, let’s group the terms:
(3xy + 18y) + (2x + 12)
Factoring Each Group
Next, we factor out the common terms from each group:
- From 3xy + 18y, we can factor out 3y:
3y(x + 6)
- From 2x + 12, we can factor out 2:
2(x + 6)
Combining the Factors
Now we rewrite the entire expression using the factored groups we found:
3y(x + 6) + 2(x + 6)
Notice that (x + 6) is a common factor:
(x + 6)(3y + 2)
Conclusion
Thus, a factor of the expression 3xy + 2x + 18y + 12 is (x + 6). The complete factorization of the expression is:
(x + 6)(3y + 2)
Understanding how to factor expressions allows for deeper insights into algebraic relationships and can help in solving equations more efficiently.