Asked by im sad
Factor 16d - 12 using the GCF.
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Answered by
GPT-4o mini
To factor the expression \(16d - 12\) using the greatest common factor (GCF), we need to identify the GCF of the coefficients 16 and 12.
1. Find the GCF of 16 and 12:
- The factors of 16 are 1, 2, 4, 8, 16.
- The factors of 12 are 1, 2, 3, 4, 6, 12.
- The common factors are 1, 2, and 4.
- The greatest of these is 4.
2. Now, factor out the GCF, which is 4:
\[
16d - 12 = 4(4d - 3)
\]
So, the factored form of \(16d - 12\) is \(4(4d - 3)\).
1. Find the GCF of 16 and 12:
- The factors of 16 are 1, 2, 4, 8, 16.
- The factors of 12 are 1, 2, 3, 4, 6, 12.
- The common factors are 1, 2, and 4.
- The greatest of these is 4.
2. Now, factor out the GCF, which is 4:
\[
16d - 12 = 4(4d - 3)
\]
So, the factored form of \(16d - 12\) is \(4(4d - 3)\).
Answered by
GPT-4o mini
Let's carefully re-evaluate the factoring of the expression \(16d - 12\).
1. **Identify the GCF:**
- The coefficients are 16 and -12.
- The factors of 16: \(1, 2, 4, 8, 16\)
- The factors of 12: \(1, 2, 3, 4, 6, 12\)
- The greatest common factor (GCF) of 16 and 12 is indeed 4.
2. **Factor out the GCF:**
- We can factor out \(4\) from the expression.
\[
16d - 12 = 4(4d) - 4(3) = 4(4d - 3)
\]
Thus, the factorization \(4(4d - 3)\) is indeed correct.
If the answer is indicated to be incorrect, it could be related to how the expression is checked or interpreted, but mathematically \(16d - 12 = 4(4d - 3)\) is correct.
If you have any specific criteria or format that needs to be followed, please let me know, and I'll be glad to assist!
1. **Identify the GCF:**
- The coefficients are 16 and -12.
- The factors of 16: \(1, 2, 4, 8, 16\)
- The factors of 12: \(1, 2, 3, 4, 6, 12\)
- The greatest common factor (GCF) of 16 and 12 is indeed 4.
2. **Factor out the GCF:**
- We can factor out \(4\) from the expression.
\[
16d - 12 = 4(4d) - 4(3) = 4(4d - 3)
\]
Thus, the factorization \(4(4d - 3)\) is indeed correct.
If the answer is indicated to be incorrect, it could be related to how the expression is checked or interpreted, but mathematically \(16d - 12 = 4(4d - 3)\) is correct.
If you have any specific criteria or format that needs to be followed, please let me know, and I'll be glad to assist!
Answered by
GPT-4o mini
I'm glad to hear that the factorization \(16d - 12 = 4(4d - 3)\) is now confirmed as correct!
To summarize:
1. **Original Expression:** \(16d - 12\)
2. **GCF Calculated:** \(4\)
3. **Factored Form:** \(4(4d - 3)\)
If you have any more questions or need further assistance, feel free to ask!
To summarize:
1. **Original Expression:** \(16d - 12\)
2. **GCF Calculated:** \(4\)
3. **Factored Form:** \(4(4d - 3)\)
If you have any more questions or need further assistance, feel free to ask!
Answered by
GPT-4o mini
Great question! Let's break down the factoring step by step to clarify how we arrived at the number 3.
Given the expression:
\[
16d - 12
\]
1. **Identify the GCF:** As noted before, the GCF of 16 and 12 is 4.
2. **Factor out the GCF:** To factor out 4 from the expression, we divide each term by 4:
- The first term is \(16d\):
\[
\frac{16d}{4} = 4d
\]
- The second term is \(-12\):
\[
\frac{-12}{4} = -3
\]
3. **Combine the factored out GCF with the new expression:**
So when we factor out the 4, we rewrite the expression as:
\[
16d - 12 = 4(4d - 3)
\]
The \(3\) comes from dividing \(-12\) by \(4\), resulting in \(-3\).
Therefore, when we factor \(16d - 12\) into \(4(4d - 3)\), we derive that number from the division of the original second term \( -12\) by the GCF \(4\).
If you have any more questions or need further clarification, feel free to ask!
Given the expression:
\[
16d - 12
\]
1. **Identify the GCF:** As noted before, the GCF of 16 and 12 is 4.
2. **Factor out the GCF:** To factor out 4 from the expression, we divide each term by 4:
- The first term is \(16d\):
\[
\frac{16d}{4} = 4d
\]
- The second term is \(-12\):
\[
\frac{-12}{4} = -3
\]
3. **Combine the factored out GCF with the new expression:**
So when we factor out the 4, we rewrite the expression as:
\[
16d - 12 = 4(4d - 3)
\]
The \(3\) comes from dividing \(-12\) by \(4\), resulting in \(-3\).
Therefore, when we factor \(16d - 12\) into \(4(4d - 3)\), we derive that number from the division of the original second term \( -12\) by the GCF \(4\).
If you have any more questions or need further clarification, feel free to ask!
Answered by
GPT-4o mini
You're welcome! I'm glad I could help. If you have any more questions in the future, whether about math or anything else, don't hesitate to ask. Have a great day!