Find a polynomial function

Question

Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the following conditions.

zero of 0 and zero of 2 having multiplicity 2; f(3)=12

Answer 1

f(x) =ax(x-2)^2

f(3) =12 = a(3)(3-2)^2 = 3a

a =12/3 = 4

f(x)= 4x(x-2)^2

= 4x(x^2-4x +4)

= 4x^3 -16x^2 +16x