To find the greatest common factor (GCF) of the expression \(3x^2 - 18x\), we start by identifying the factors of each term:
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The first term is \(3x^2\).
- Factors: \(3\) and \(x^2\)
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The second term is \(-18x\).
- Factors: \(-18\) and \(x\)
Next, we find the GCF of the coefficients \(3\) and \(-18\):
- The factors of \(3\) are \(1, 3\).
- The factors of \(-18\) are \(-1, -18, 1, 2, 3, 6, 9, 18\).
The greatest common factor of \(3\) and \(-18\) is \(3\).
Now, for the variable part, we identify the smallest power of \(x\) present in both terms. In \(3x^2\), we have \(x^2\), and in \(-18x\), we have \(x\). The minimum power is \(x^1\).
Combining the GCF of the coefficients with the variable part, we get:
\[ \text{GCF} = 3x \]
Thus, the greatest common factor of the expression \(3x^2 - 18x\) is \(3x\).
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