Factor Polynomials

As f(x) is divisible by (x-1), so it can be written as :
f(x) = (x-1) * q(x)
where q(x) is the quotient.

By putting x = 2x+1, we have,
f(2x+1) = (2x+1-1) * q(2x+1)
that is,
f(2x+1) = 2x * q(2x+1)
that means 2, x, and q(2x+1) are the factors of f(2x+1).
therefore, the answer is (A).