To determine which expression is a factor of 2xy + 6x + 3y + 9, we first need to look for common factors among the terms. Let’s break down each term:
- The first term is 2xy.
- The second term is 6x.
- The third term is 3y.
- The fourth term is 9.
Now, let’s look for the greatest common factor (GCF) of these terms. The coefficients of the numeric terms (2, 6, 3, and 9) have a GCF of 1. When we check the variable components, we see:
- 2xy contains both x and y.
- 6x contains x only.
- 3y contains y only.
- 9 is a constant term.
Since the terms do not share any common factors among the variables, the only significant common factor throughout the entire expression is 1. This means that we cannot factor out any expression other than 1.
Thus, we can conclude that in the context of typical factorization, there isn’t a specific algebraic expression that can be factored out of 2xy + 6x + 3y + 9 other than the trivial factor of 1.
However, if the question was to simplify or express it in a different way, we could consider grouping terms or rearranging them, but that would not yield a common factor as well.