Question
hich of the following is the GCF of the polynomial 3x^4+3x^3−9x^2+12x ?
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\), we first identify the coefficients and the variable parts of each term:
1. The terms are:
- \(3x^4\)
- \(3x^3\)
- \(-9x^2\)
- \(12x\)
2. **Finding the GCF of the coefficients:**
- The coefficients are 3, 3, -9, and 12.
- The GCF of \(3, 3, -9, 12\) is 3.
3. **Finding the GCF of the variable parts:**
- The variable parts are \(x^4\), \(x^3\), \(x^2\), and \(x\).
- The GCF of \(x^4, x^3, x^2, x\) is \(x^1\) or simply \(x\).
4. **Combining the GCFs:**
- The overall GCF of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\) is the product of the GCF of the coefficients and the GCF of the variable parts, which is:
\[
\text{GCF} = 3x.
\]
Therefore, the GCF of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\) is \(\boxed{3x}\).
1. The terms are:
- \(3x^4\)
- \(3x^3\)
- \(-9x^2\)
- \(12x\)
2. **Finding the GCF of the coefficients:**
- The coefficients are 3, 3, -9, and 12.
- The GCF of \(3, 3, -9, 12\) is 3.
3. **Finding the GCF of the variable parts:**
- The variable parts are \(x^4\), \(x^3\), \(x^2\), and \(x\).
- The GCF of \(x^4, x^3, x^2, x\) is \(x^1\) or simply \(x\).
4. **Combining the GCFs:**
- The overall GCF of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\) is the product of the GCF of the coefficients and the GCF of the variable parts, which is:
\[
\text{GCF} = 3x.
\]
Therefore, the GCF of the polynomial \(3x^4 + 3x^3 - 9x^2 + 12x\) is \(\boxed{3x}\).