Can you provide the answer to this problem?

Question

Sketch the graph with zeros at -2, 1 (multiplicity of 3), 5 with lowest odd degree for given zeros without a stated multiplicity and negative leading coefficient. Write your polynomial in factored form.

Answer 1

The polynomial would be y = -a (x+2) (x-1)³ (x-5) because the middle term has multiplicity 3. This would rise from the left, cross the x-axis at -2, reach a relative maximum between there and x = 1, have an inflection point at x = 1 where the slope which has been negative goes to zero, then back to negative in order to reach a relative minimum between x = 1 and x = 5, where it crosses the x-axis in order to zoom off to positive infinity.