To factor out the greatest common factor (GCF) from the polynomial \(4y^3 - 16y^2\), we first identify the GCF of the terms \(4y^3\) and \(-16y^2\).
The coefficients are 4 and -16. The GCF of 4 and 16 is 4.
For the variable part, the lowest power of \(y\) present in the terms is \(y^2\).
Thus, the GCF of the entire expression is \(4y^2\).
Now we can factor \(4y^2\) out of the polynomial:
\[ 4y^2(y - 4) \]
So, the factored form is:
\[ 4y^2(y - 4) \]