To factor out the greatest common factor (GCF) from the polynomial \(12a^3 - 18a^2\), we first identify the GCF of the coefficients and the variable parts.
- The coefficients are 12 and -18. The GCF of 12 and 18 is 6.
- For the variable part, both terms have \(a^2\) as a common factor since \(a^3\) and \(a^2\) both contain \(a^2\).
Therefore, the GCF of the entire expression is \(6a^2\).
Now, we can factor that out:
\[ 12a^3 - 18a^2 = 6a^2(2a - 3) \]
So, the factored form of the polynomial is:
\[ 6a^2(2a - 3) \]