Function Root Behaviour (Polynomials) - Behaviour to Roots and Multiplicity

Question

What roots and multiplicities would create this x-intercept behaviour?

$$	ext{at }x=-3	ext{: touches the x-axis without crossing} \ 	ext{at }x=0	ext{: crosses the x-axis and flattens} \$$

Accepted Answer

$$x=-3 	ext{ (multiplicity 2)} \ x=0 	ext{ (multiplicity 3)} \$$

Answer

$$x=-3 	ext{ (multiplicity 3)} \ x=0 	ext{ (multiplicity 3)} \$$

Answer

$$x=0 	ext{ (multiplicity 3)} \ x=3 	ext{ (multiplicity 2)} \$$

Answer

$$x=2 	ext{ (multiplicity 1)} \ x=3 	ext{ (multiplicity 1)} \$$

Answer

$$x=-3 	ext{ (multiplicity 3)} \ x=0 	ext{ (multiplicity 2)} \$$