Constructing a Polynomial with 5th Degree

Question

Construct a fifth degree polynomial where 1 is a zero of multiplicity 3 and 2𝑖 is a root. (Multiplied out,
not factored)

Answer 1

f(x) = (x-1)³[(x-2i)(x+2i)

 

      = (x³-3x²+3x-1)(x²+4) 

 

and I let you finish the job (use polynomial 'long' multiplication)