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To determine which expression does not have a Greatest Common Factor (GCF), let's analyze each option:

1. **\(9x^2 - 16\)**  
   This expression is a difference of squares: \(9x^2 - 16 = (3x + 4)(3x - 4)\). There is no GCF other than 1 in the original expression.

2. **\(2x^2 + 8x + 4\)**  
   Here, each term has a common factor of 2. Factoring out 2 gives:  
   \(2(x^2 + 4x + 2)\).

3. **\(3x^2 - 12\)**  
   Each term has a common factor of 3. Factoring out 3 gives:  
   \(3(x^2 - 4)\).

4. **\(9x^4 + 2x^2 + 7x\)**  
   Each term contains an \(x\) term except the constant term 7, but no common factor for all terms exists. So, it has no GCF other than 1.

Thus, the answer is the last option: **\(9x^4 + 2x^2 + 7x\)**, which does not have a GCF.

Would you like further details on how the factoring was done, or do you have any additional questions?

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### Additional Questions to Explore:
1. What is the process for identifying the GCF of an expression?
2. How can we factor a difference of squares?
3. How do we factor polynomials with three or more terms?
4. What is the distributive property in the context of factoring?
5. How can GCF help in simplifying polynomial expressions?

**Tip:** When looking for the GCF, check each term for the smallest shared factor.

Which expression does NOT have a Greatest Common Factor?

Explore how to identify expressions that do not have a Greatest Common Factor (GCF). This problem covers algebraic concepts including factoring and the difference of squares, suitable for students in Grades 8-10.

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