The graph of a polynomial meets the x-axis at -3, 0 and 2, and nowhere else.

Step 1. The zeroes. $-3$, $0$ and $2$.

Step 2. The degree. A polynomial of degree $n$ has at most $n$ zeroes, so three zeroes need a degree of at least $3$.

Step 3. One example. $x(x + 3)(x - 2) = x^3 + x^2 - 6x$.