The expression provided is $14x + 7$. To factor this expression completely, we need to find the greatest common factor (GCF) of the terms.

1. Identify the GCF: The GCF of 14 and 7 is 7.
2. Factor out the GCF: We can factor out 7 from the expression.

So, $14x + 7$ can be factored as: $14x + 7 = 7(2x + 1)$

To check by multiplying, distribute the 7 back into the expression: $7(2x + 1) = 7 \times 2x + 7 \times 1 = 14x + 7$ This confirms that the factorization is correct.

Would you like more details on this, or do you have any questions?

Here are 5 related questions to further explore:

1. How do you factor expressions with more than two terms?
2. What is the difference between factoring completely and partially?
3. Can you factor a quadratic expression like $x^2 + 5x + 6$?
4. How would you factor the expression $14x - 7$?
5. What are common mistakes to avoid when factoring expressions?

Tip: Always double-check your factorization by distributing back to ensure the original expression is obtained.