To factor the expression \(6x + 18x^2\) by finding the greatest common factor (GCF), we first identify the GCF of the two terms.
The terms are:
- \(6x\)
- \(18x^2\)
The GCF of \(6x\) and \(18x^2\) is \(6x\).
Now, we factor \(6x\) out of the expression:
\[ 6x + 18x^2 = 6x(1 + 3x) \]
So the correct factored form of the expression is:
\[ 6x(1 + 3x) \]
Thus, the answer is: 6x (1 + 3x)