Answer :
Sure, let's analyze the expression \(12d - 26c\) to determine which statements about rewriting it as a product are accurate and relevant.
### Identifying the Greatest Common Factor (GCF)
First, we observe the coefficients of the terms:
- The coefficient of \(d\) is 12.
- The coefficient of \(c\) is 26.
To find the GCF of 12 and 26, consider the factors of each number:
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 26: \(1, 2, 13, 26\)
The greatest common factor (GCF) is the largest number that appears in both lists of factors. Here, the GCF of 12 and 26 is 2.
### Factoring the Expression
Given the GCF is 2, we can factor the expression \(12d - 26c\) as follows:
[tex]\[ 12d - 26c = 2(6d - 13c) \][/tex]
### Let's Analyze the Options
1. The GCF of the numbers in each term in the expression is 2.
- This statement is accurate. We identified that the GCF of 12 and 26 is indeed 2.
2. The GCF of the numbers in each term in the expression is 4.
- This statement is not accurate. We determined the GCF to be 2, not 4.
3. The GCF of the variables in each term in the expression is \(cd\).
- This statement is not relevant since the variables \(d\) and \(c\) do not have common factors (they are for different terms).
4. The factored expression is \(2(6d - 13c)\).
- This statement is accurate. The expression \(12d - 26c\) can be factored into \(2(6d - 13c)\).
5. The factored expression is \(2 \operatorname{cod}(6 - 13)\).
- This statement does not make sense in the context of factoring algebraic expressions and contains elements that are not algebraically correct.
### Conclusion
The accurate and relevant statements about rewriting \(12d - 26c\) as a product are:
- The GCF of the numbers in each term in the expression is 2.
- The factored expression is [tex]\(2(6d - 13c)\)[/tex].
### Identifying the Greatest Common Factor (GCF)
First, we observe the coefficients of the terms:
- The coefficient of \(d\) is 12.
- The coefficient of \(c\) is 26.
To find the GCF of 12 and 26, consider the factors of each number:
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 26: \(1, 2, 13, 26\)
The greatest common factor (GCF) is the largest number that appears in both lists of factors. Here, the GCF of 12 and 26 is 2.
### Factoring the Expression
Given the GCF is 2, we can factor the expression \(12d - 26c\) as follows:
[tex]\[ 12d - 26c = 2(6d - 13c) \][/tex]
### Let's Analyze the Options
1. The GCF of the numbers in each term in the expression is 2.
- This statement is accurate. We identified that the GCF of 12 and 26 is indeed 2.
2. The GCF of the numbers in each term in the expression is 4.
- This statement is not accurate. We determined the GCF to be 2, not 4.
3. The GCF of the variables in each term in the expression is \(cd\).
- This statement is not relevant since the variables \(d\) and \(c\) do not have common factors (they are for different terms).
4. The factored expression is \(2(6d - 13c)\).
- This statement is accurate. The expression \(12d - 26c\) can be factored into \(2(6d - 13c)\).
5. The factored expression is \(2 \operatorname{cod}(6 - 13)\).
- This statement does not make sense in the context of factoring algebraic expressions and contains elements that are not algebraically correct.
### Conclusion
The accurate and relevant statements about rewriting \(12d - 26c\) as a product are:
- The GCF of the numbers in each term in the expression is 2.
- The factored expression is [tex]\(2(6d - 13c)\)[/tex].
