Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, −4 is the only other zero, leading coefficient is 2.

Answer 1

Since the polynomial has degree 5, the sum of the multiplicities must be 5.

We know that 2 has multiplicity 3

So, since -4 is the only other zero, -4 must have multiplicity 2.

f(x) = 2(x-2)³(x+4)²

Answer 2

P(x) = (x-2)^3(x+4)(2x-k)