Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 353: 67

$f(x)=(x+1)^3(x-1)^3$

Step 1. Identify zeros from the graph: $x=-1,-1,-1,1,1,1$ Step 2. Write a form of the polynomial: $f(x)=k(x+1)^3(x-1)^3$ where $k$ is unknown. Step 3. As point $(0,-1)$ is on the curve, we have $f(0)=k(0+1)^3(0-1)^3=-1$, thus $k=1$ Step 4. $f(x)=(x+1)^3(x-1)^3$