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Question
Which of the following is the GCF of the polynomial 4x4+12x3−36x2+24x ?(1 point)
Responses
4x
4 x
4
4
2x
2 x
6x
Answers
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Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the polynomial \(4x^4 + 12x^3 - 36x^2 + 24x\), we can factor out the common terms.
1. **Identify the coefficients:**
- The coefficients are 4, 12, -36, and 24. The GCF of these numbers is 4.
2. **Identify the variable part:**
- The terms have \(x^4\), \(x^3\), \(x^2\), and \(x\). The lowest power of \(x\) among these terms is \(x\).
3. **Combine the GCF of the coefficients with the GCF of the variable parts:**
- Thus, the GCF of the entire polynomial is \(4x\).
So the GCF of the polynomial \(4x^4 + 12x^3 - 36x^2 + 24x\) is **4x**.
1. **Identify the coefficients:**
- The coefficients are 4, 12, -36, and 24. The GCF of these numbers is 4.
2. **Identify the variable part:**
- The terms have \(x^4\), \(x^3\), \(x^2\), and \(x\). The lowest power of \(x\) among these terms is \(x\).
3. **Combine the GCF of the coefficients with the GCF of the variable parts:**
- Thus, the GCF of the entire polynomial is \(4x\).
So the GCF of the polynomial \(4x^4 + 12x^3 - 36x^2 + 24x\) is **4x**.
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