Answer
$f(x)=-(x+3)(x+2)(x+1)(x-1)(x-2) $
See graph.
Work Step by Step
Step 1. The end behavior can be identified as $x\to-\infty, y\to\infty$ and $x\to\infty, y\to-\infty$
Thus the leading coefficient should be negative and the power should be odd.
Step 2. There are $4$ turning points. Thus we have $n=5$ as the degree of the polynomial.
Step 3. We can write an example polynomial as $f(x)=-(x+3)(x+2)(x+1)(x-1)(x-2)=-(x+3)(x^2-4)(x^2-1) $
Step 4. See graph for the above function.
