The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−4

Question

A) The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at  x=2 and  x=0, and a root of multiplicity 1 at x=−4 Find a possible formula for 

P(x)=

B) Find a degree 3 polynomial having zeros -7, 4 and 8 and the coefficient of x^3 equal 1. The polynomial is

Answer 1

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

b) Q(x) = (x+7)(x-4)(x-8)