To factor out the greatest common factor (GCF) from the polynomial \(10s^3 + 6s^2\), we first need to find the GCF of the coefficients and the variable terms.
The coefficients are 10 and 6. The GCF of 10 and 6 is 2.
For the variable \(s\), the smallest power of \(s\) in the terms is \(s^2\).
Thus, the GCF of the entire expression is \(2s^2\).
Now, we can factor out \(2s^2\) from the polynomial:
\[ 10s^3 + 6s^2 = 2s^2(5s + 3) \]
So the factored form is:
\[ 2s^2(5s + 3) \]