Math question (Algebra)

Question

Construct a polynomial function with the following: fifth degree, 2 is a zero of multiplicity 3. -2 is the only other zero. leading coefficient is 2.

Answer. f(x) =

Answer 1

If 2 is a zero of multiplicity 3, that means (x-2)^3 is a factor. And if -2 is the only other zero, then the other factor must be (x+2)^2. Altogether the expanded form must be of degree 5.

f(x) = 2(x-2)^3(x+2)^2