Answer
$\{ \pm\frac{1}{2}, \pm 4 \}$
Work Step by Step
Step 1. Factor the polynomial $f(x)=(4x^2-1)(x^2-16)$
Step 2. For $4x^2-1=0$, we have $x=\pm\frac{1}{2}$
Step 3. For $x^2-16=0$, we have $x=\pm 4$
Step 4. The zeros are $\{ \pm\frac{1}{2}, \pm 4 \}$