Which of the following is the sum of $2{\mathrm{x}}^3-9{\mathrm{x}}^2+8, 3{\mathrm{x}}^2-6\mathrm{x}-5, 7{\mathrm{x}}^3-10\mathrm{x}+1$ and $3+2\mathrm{x}-5{\mathrm{x}}^2-4{\mathrm{x}}^3$?

The given expressions are,
$2{\mathrm{x}}^3-9{\mathrm{x}}^2+8, 3{\mathrm{x}}^2-6\mathrm{x}-5,7 {\mathrm{x}}^3-10\mathrm{x}+1$ and $3+2\mathrm{x}-5{\mathrm{x}}^2-4{\mathrm{x}}^3$ .
Add each term of given expressions, 

$\Rightarrow (2{\mathrm{x}}^3-9{\mathrm{x}}^2+8)+(3{\mathrm{x}}^2-6\mathrm{x}-5)+(7{\mathrm{x}}^3-10\mathrm{x}+1)+(3+2\mathrm{x}-5{\mathrm{x}}^2-4{\mathrm{x}}^3)$

Putting like terms together

$\Rightarrow (2{\mathrm{x}}^3+7{\mathrm{x}}^3-4{\mathrm{x}}^3)+(-9{\mathrm{x}}^2+3{\mathrm{x}}^2-5{\mathrm{x}}^2)+(-6\mathrm{x}-10\mathrm{x}+2\mathrm{x})+(8-5+1+3)$  

Take ${\mathrm{x}}^3, {\mathrm{x}}^2$, and $\mathrm{x}$ common from the expressions,we get,

$\Rightarrow {\mathrm{x}}^3(2+7-4)+{\mathrm{x}}^2(-9+3-5)+\mathrm{x}(-6-10+2)+(8-5+1+3)$ 

$\Rightarrow {\mathrm{x}}^3\left(5\right)+{\mathrm{x}}^2(-11)+\mathrm{x}(-14)+\left(7\right)$    

$\Rightarrow 5{\mathrm{x}}^3-11{\mathrm{x}}^2-14\mathrm{x}+7$ 

Hence, the sum of $\mathbf{2}{\mathbf{x}}^{\mathbf{3}}\mathbf{-}\mathbf{9}{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{8}\mathbf{,}\mathbf{3}{\mathbf{x}}^{\mathbf{2}}\mathbf{-}\mathbf{6}\mathbf{x}\mathbf{-}\mathbf{5}\mathbf{,}\mathbf{7}{\mathbf{x}}^{\mathbf{3}}\mathbf{-}\mathbf{10}\mathbf{x}\mathbf{+}\mathbf{1}$ and $\mathbf{3}\mathbf{+}\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{5}{\mathbf{x}}^{\mathbf{2}}\mathbf{-}\mathbf{4}{\mathbf{x}}^{\mathbf{3}}$ is equal to$\mathbf{5}{\mathbf{x}}^{\mathbf{3}}\mathbf{-}\mathbf{11}{\mathbf{x}}^{\mathbf{2}}\mathbf{-}\mathbf{14}\mathbf{x}\mathbf{+}\mathbf{7}$.