To simplify the polynomial 4x^2 + 4 - 5x + x - 2x^2 + 8, first rewrite it to put all the like terms next to one another: 4x^2 - 2x^2 - 5x + x + 4 + 8. Then, add together these like terms: 2x^2 - 4x + 12. So, the correct answer will be the last option.