How can I factor this polynomial out

I'm trying to find the zeros for this polynomial, but I can't seem to get them right. Help please! :)
5x^3 + 19x^2 +16x -4

Look at the graph or use the rational roots theorem to find the root at x = -2.
Use the factor theorem to convert this root into a factor: (x + 2)
Divide the original function by the known factor:
(5x^3 + 19x^2 +16x -4) / (x + 2) = 5x^2 + 9x - 2
Factor the reduced quadratic:
(x + 2) (5x - 1)
So altogether the factorization of 5x^3 + 19x^2 +16x -4 is:
(x + 2)^2 (5x - 1)