Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 186: 118

$f(x)=x^3(x+4)(x-2)$

Step 1. Use the given zeros and multiplicities, we can write a general form of the function as $f(x)=ax^3(x+4)(x-2)$ where $a$ is unknown. Step 2. With known point $(-2,64)$ on the curve, we have $f(-2)=a(-2)^3(-2+4)(-2-2)=64$, thus $a=1$ Step 3. Thus the function is $f(x)=x^3(x+4)(x-2)$