To factor out the greatest common factor (GCF) from the polynomial \(3d^3 + 6d^2\), we first identify the GCF of the coefficients (3 and 6) and the variable parts.
The GCF of the coefficients 3 and 6 is 3. For the variable part, the smallest power of \(d\) in both terms is \(d^2\).
Thus, the GCF of the entire expression is \(3d^2\).
Now we can factor \(3d^2\) out of the polynomial:
\[ 3d^3 + 6d^2 = 3d^2(d + 2) \]
So, the factored form is:
\[ 3d^2(d + 2) \]