Complex Numbers and Quadratic Equations

Let R denote the set of all real numbers. Let ai, bi R for i \1, 2, 3\. Define the functions f: R R, g: R R, and h: R R by f(x) = a1 + 10x + a2x2 + a3x3 + x4, g(x) = b1 + 3x + b2x2 + b3x3 + x4, h(x) = f(x+1) - g(x+2). If f(x) g(x) for every x R, then the coefficient of x3 in h(x) is

1. 8
2. 2
3. -4
4. -6