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