Question
−15x2, 35x3 what is gcf
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the expressions \(-15x^2\) and \(35x^3\), we can follow these steps:
1. **Factor the coefficients:**
- The coefficients are \(-15\) and \(35\).
- The prime factorization of \(-15\) is \(-1 \times 3 \times 5\).
- The prime factorization of \(35\) is \(5 \times 7\).
- The common factor between \(-15\) and \(35\) is \(5\).
2. **Factor the variable parts:**
- The variable parts are \(x^2\) and \(x^3\).
- The GCF of \(x^2\) and \(x^3\) is \(x^2\) (since we take the lowest power of \(x\)).
3. **Combine the GCFs:**
- Combine the GCF of the coefficients (\(5\)) with the GCF of the variable parts (\(x^2\)):
- Therefore, the GCF of \(-15x^2\) and \(35x^3\) is \(5x^2\).
So, the GCF is \(5x^2\).
1. **Factor the coefficients:**
- The coefficients are \(-15\) and \(35\).
- The prime factorization of \(-15\) is \(-1 \times 3 \times 5\).
- The prime factorization of \(35\) is \(5 \times 7\).
- The common factor between \(-15\) and \(35\) is \(5\).
2. **Factor the variable parts:**
- The variable parts are \(x^2\) and \(x^3\).
- The GCF of \(x^2\) and \(x^3\) is \(x^2\) (since we take the lowest power of \(x\)).
3. **Combine the GCFs:**
- Combine the GCF of the coefficients (\(5\)) with the GCF of the variable parts (\(x^2\)):
- Therefore, the GCF of \(-15x^2\) and \(35x^3\) is \(5x^2\).
So, the GCF is \(5x^2\).