jmc

The sum of the coefficients in $3(x^{10}-x^7+2x^3-x+7)+4(x^3-2x^2-5)$ is $3(1-1+2-1+7)+4(1-2-5)=3\cdot 8+4\cdot (-6)=\boxed{0}$. (The sum of the coefficients in a polynomial can be found by setting the variable to 1.)