Chapter 3 - Polynomial and Rational Functions - 3.3 Zeros of Polynomial Functions - 3.3 Exercises - Page 338: 115

$\{ \pm2, \pm 3, \pm 2i \}$

Step 1. Factor the polynomial $f(x)=x^4(x^2-9)-16(x^2-9)=(x^2-9)(x^4-16)=(x^2-9)(x^2-4)(x^2+4)$ Step 2. For $x^2-9=0$, we have $x=\pm 3$ Step 3. For $x^2-4=0$, we have $x=\pm 2$ Step 4. For $x^2+4=0$, we have $x=\pm 2i$ Step 5. The zeros are $\{ \pm2, \pm 3, \pm 2i \}$