#### Answer

The simplified form is $2{{x}^{3}}-5{{x}^{2}}-3x+6$

#### Work Step by Step

The divisor is $x-4$ and in synthetic division, the divisor should be in $x\ -\ c$ form. Therefore, synthetic division can be applied to the given problem
Apply synthetic division as:
$\begin{matrix}
4 & 2 & -13 & 17 & 18 & -24 \\
{} & {} & 8 & -20 & -12 & 24 \\
{} & 2 & -5 & -3 & 6 & 0 \\
\end{matrix}$.
Thus, the quotient is $2{{x}^{3}}-5{{x}^{2}}-3x+6$ , and the remainder is 0.
By the synthetic method $\frac{2{{x}^{4}}-13{{x}^{3}}+17{{x}^{2}}+18x-24}{x-4}$ is $2{{x}^{3}}-5{{x}^{2}}-3x+6$.