Final answer:
The expression that represents the next consecutive integer after 3x² + 1 is 3x² + 2. This is obtained by adding one to the original expression to account for the step to the next integer.
Step-by-step explanation:
If the expression 3x² + 1 represents an integer, then the expression representing the next consecutive integer would simply be this expression plus one. Therefore, the next consecutive integer can be expressed as (3x² + 1) + 1, which simplifies to 3x² + 2.
To understand why this is the case, it's important to remember that consecutive integers are numbers that follow each other in order without any gaps. For example, if 3x² + 1 is equal to some integer n, then the next consecutive integer is n + 1. We apply this same logic to the expression 3x² + 1 to find its consecutive integer. Since adding one to an integer will always result in the next integer, we simply add one to the entire expression 3x² + 1 to achieve this.