The expression to factor is:

$4z^3 - 16z$

Step 1: Factor out the greatest common factor (GCF)

The greatest common factor of $4z^3$ and $16z$ is $4z$. Factor this out:

$4z(z^2 - 4)$

Step 2: Factor the remaining quadratic expression

The expression $z^2 - 4$ is a difference of squares, which can be factored as:

$z^2 - 4 = (z - 2)(z + 2)$

Final Factored Form:

$4z(z - 2)(z + 2)$

So, the completely factored form of the expression is:

$4z(z - 2)(z + 2)$

Would you like more details on factoring techniques or have any questions?

Here are 5 related questions:

1. How do you find the greatest common factor (GCF)?
2. What is the difference of squares, and how do you recognize it?
3. Can you always factor a quadratic expression this way?
4. How does factoring help in solving equations?
5. What happens if you try to factor a sum of squares?

Tip: Always start by looking for the greatest common factor (GCF) when factoring any expression.