"Find the factorization of 2x^4+5x^3-20x^2-35x-12 if 2x+1 is one of its factors"

I divide and get x^3 + 2x^2 - 11x - 12 but my answer choices are completely different, stuff like (2x + 1) (x + 4) (x + 3) (x - 1). I believe I have to factor my answer, but I'm not sure how to go about. All my teacher said was to divide the the polynomial by the term and that's all.