https://file.aiquickdraw.com/mathbot/file/173021226596069xm99ey.jpg

To determine which expression does **not** have a Greatest Common Factor (GCF) other than 1, we’ll analyze each option.

1. **\( 3x^2 - 12 \):**
   - Terms: \( 3x^2 \) and \( -12 \)
   - The GCF is 3 since both terms are divisible by 3.

2. **\( 9x^4 + 2x^2 + 7x \):**
   - Terms: \( 9x^4 \), \( 2x^2 \), and \( 7x \)
   - Checking factors, there is no common factor across all terms other than 1. Therefore, this expression has no GCF other than 1.

3. **\( 2x^2 + 8x + 4 \):**
   - Terms: \( 2x^2 \), \( 8x \), and \( 4 \)
   - The GCF is 2, as each term is divisible by 2.

4. **\( 9x^2 - 16 \):**
   - Terms: \( 9x^2 \) and \( -16 \)
   - The GCF is 1 because 9 and 16 share no common factors.

Thus, **option B (\( 9x^4 + 2x^2 + 7x \))** is the correct answer, as it does not have a GCF other than 1. Your original answer was correct.

Would you like more details or have any questions?

---

Here are 5 related questions to consider:
1. How do you find the GCF of polynomial terms?
2. Why is finding the GCF important in simplifying expressions?
3. How does the distributive property relate to factoring out the GCF?
4. Can all polynomial expressions have a GCF?
5. How do constants affect the GCF of polynomial expressions?

**Tip:** Always check each term individually to ensure no common factor other than 1 exists across all terms in a polynomial.

Which expression does NOT have a Greatest Common Factor?

Learn how to determine if a polynomial has a Greatest Common Factor (GCF) other than 1. This problem explores factoring concepts and is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation