Let $ℝ$ denote the set of all real numbers. Let $a_i,b_i\in ℝ\text{for}i\in \{1,2,3\}$.

Define the functions $f:ℝ\to ℝ$, $g:ℝ\to ℝ$, and $h:ℝ\to ℝ$ by

$f\left(x\right)=a_1+10x+a_2{x}^2+a_3{x}^3+x^4$

$g\left(x\right)=b_1+3x+b_2{x}^2+b_3{x}^3+x^4$

$h\left(x\right)=f(x+1)-g(x+2)$

If $f\left(x\right)=g\left(x\right)$ for every $x\in ℝ$, then the coefficient of $x^3$ in $h\left(x\right)$ is