Let \( \mathbb{R} \) denote the set of all real numbers. Let \( a_i, b_i \in \mathbb{R} \) for \( i \in \{1,2,3\} \). Define the functions \( f : \mathbb{R} \to \mathbb{R},\ g : \mathbb{R} \to \mathbb{R} \) and \( h : \mathbb{R} \to \mathbb{R} \) by
\( f(x)=a_1+10x+a_2x^2+a_3x^3+x^4 \), \( g(x)=b_1+3x+b_2x^2+b_3x^3+x^4 \), \( h(x)=f(x+1)-g(x+2) \).
If \( f(x)\neq g(x) \) for every \( x\in\mathbb{R} \), then the coefficient of \( x^3 \) in \( h(x) \) is:
