Short Answer 
None of the expressions listed are divisible by (x + 2b) as all resulted in non-zero remainders when performing polynomial division, thus confirming that (x + 2b) is not a factor of any provided expression.
Step 1: Identify the Expressions
We start by listing the expressions we need to evaluate for the factor (x + 2b). The expressions are:
- Expression A: (3x² + 7x + 14b)
- Expression B: (3x² + 16x + 14b)
- Expression C: (3x² + 18x + 14b)
- Expression D: (3x² + 25x)
Step 2: Perform Polynomial Division
For each expression, we carry out the polynomial division by (x + 2b) to check if it divides evenly. We are looking for a zero remainder, which indicates that (x + 2b) is a factor:
- Expression A: Non-zero remainder.
- Expression B: Non-zero remainder.
- Expression C: Non-zero remainder.
- Expression D: Non-zero remainder.
Step 3: Conclusion
After performing the division on all expressions, we find that none result in a zero remainder. Therefore, we conclude that (x + 2b) is not a factor of any of the provided expressions.