Answer
$2x^2-7x+14+\dfrac{-20}{x+2}$
Work Step by Step
Equating to zero the divisor of the given expression, $( 2x^3-3x^2+8 )\div( x+2 ) ,$ and then solving for the variable, result to \begin{align*} x+2&=0 \\ x&=-2 .\end{align*} Using $ -2 $ in operating the coefficients of the dividend through synthetic division gives the result shown below. The last row of numbers, $\left\{ 2,-7,14,-20 \right\},$ gives the coefficient of the quotient and the remainder. Hence, $( 2x^3-3x^2+8 )\div( x+2 ) $ is equal to \begin{align*} 2x^2-7x+14+\dfrac{-20}{x+2} .\end{align*}