Which subset of $$ A $$ has a GCF of the elements that is $$ 2 x $$ ? A. $$ \{2 x, 4 x, 12 x y\} $$ B. $$ \{2 x, 4 x, 5 x y, 7 x, 12 x y, 13 x, 15 x\} $$ C. $$ \{4 x, 12 x y\} $$ D. $$ \{2 x, 5 x y, 12 x y\} $$ Video Textbook Get more heln

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To determine which subset of $$ A $$ has a **Greatest Common Factor (GCF)** of $$ 2x $$, let's analyze each option:

### **Option A: $$ \{2x, 4x, 12xy\} $$**
- **Factors:**
  - $$ 2x = 2 	imes x $$
  - $$ 4x = 2 	imes 2 	imes x $$
  - $$ 12xy = 2 	imes 2 	imes 3 	imes x 	imes y $$
- **Common Factors:** 
  - $$ 2 	imes x $$
- **GCF:** $$ 2x $$

### **Option B: $$ \{2x, 4x, 5xy, 7x, 12xy, 13x, 15x\} $$**
- **Factors:**
  - $$ 2x = 2 	imes x $$
  - $$ 4x = 2 	imes 2 	imes x $$
  - $$ 5xy = 5 	imes x 	imes y $$
  - $$ 7x = 7 	imes x $$
  - $$ 12xy = 2 	imes 2 	imes 3 	imes x 	imes y $$
  - $$ 13x = 13 	imes x $$
  - $$ 15x = 3 	imes 5 	imes x $$
- **Common Factors:** 
  - Only $$ x $$ is common to all.
- **GCF:** $$ x $$ (Not $$ 2x $$)

### **Option C: $$ \{4x, 12xy\} $$**
- **Factors:**
  - $$ 4x = 2 	imes 2 	imes x $$
  - $$ 12xy = 2 	imes 2 	imes 3 	imes x 	imes y $$
- **Common Factors:** 
  - $$ 2 	imes 2 	imes x = 4x $$
- **GCF:** $$ 4x $$ (Not $$ 2x $$)

### **Option D: $$ \{2x, 5xy, 12xy\} $$**
- **Factors:**
  - $$ 2x = 2 	imes x $$
  - $$ 5xy = 5 	imes x 	imes y $$
  - $$ 12xy = 2 	imes 2 	imes 3 	imes x 	imes y $$
- **Common Factors:** 
  - Only $$ x $$ is common to all.
- **GCF:** $$ x $$ (Not $$ 2x $$)

### **Conclusion**
Only **Option A** has a GCF of $$ 2x $$.

**Answer:** A. $$ \{2x, 4x, 12xy\} $$
The subset with a GCF of $$ 2x $$ is $$ \{2x, 4x, 12xy\} $$.

Which subset of has a GCF of the elements that is ?
A.
B.
C.
D.
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Option A:

Option B:

Option C:

Option D:

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Which subset of has a GCF of the elements that is ? A. B. C. D. Video Textbook Get more heln