Find a polynomial function of degree 5 with minus3 as a zero of multiplicity​ 3, 0 as a zero of multiplicity 1​, and 3 as a zero of multiplicity 1.

Answer 1

(-3) came from the factor (x+3), since it has multiplicity of 3 you have to account for that zero 3 times, therefore it is written as (x+3)³.

0 as a zero comes from the factor x.

3 comes from the factor (x-3).

The polynomial function in factored form is f(x)=x(x+3)³ (x-3)

*Make sure the number of zeros equals the degree of the polynomial!