Question

Find a polynomial f(x) of degree 4 whose coefficients are integers, such that the constant term is -1, 1/2 is a root of multiplicity 2, and 2x^2-4x-1 is a factor of f(x).

Answer 1

How about:
f(x)=a(2x-1)^2(2x^2-4x-1)
where a is an integer constant.