To factor out the greatest common factor (GCF) from the polynomial \(3c^3 + 6c^2\), we first identify the GCF of the coefficients and the common factors in the terms.
The coefficients are 3 and 6. The GCF of 3 and 6 is 3.
For the variable part, we have \(c^3\) and \(c^2\). The GCF for \(c^3\) and \(c^2\) is \(c^2\).
Now, we can factor out the GCF, which is \(3c^2\):
\[ 3c^3 + 6c^2 = 3c^2(c + 2) \]
So, the factored form is:
\[ 3c^2(c + 2) \]