To factor out the greatest common factor (GCF) from the polynomial \(5p^3 + 15p^2\), we first identify the GCF of the coefficients and the variable terms.
- The coefficients are 5 and 15. The GCF of these numbers is 5.
- For the variable terms, we have \(p^3\) and \(p^2\). The GCF of \(p^3\) and \(p^2\) is \(p^2\).
Now we can factor out the GCF of \(5p^2\):
\[ 5p^3 + 15p^2 = 5p^2(p + 3) \]
So, the factored form of the polynomial is:
\[ 5p^2(p + 3) \]