So it has a root at x = 2, which means x - 2 = 0. Therefore, x - 2 is a factor. It's also repeated, so (x - 2)^2 is a factor.

Similarly, it has a root at x = 0, which means x is a factor. It's repeated, so x^2 is a factor.

Similarly, it has a root at x = -4, which means x + 4 = 0. Therefore, x + 4 is a factor.

So P(x) = x^2(x - 2)^2(x + 4) is a possible formula. So is any constant multiple.