Answer
$x^5+5x^4+8x^3+16x^2+33x+63+\dfrac{128}{x-2}$
Work Step by Step
We have to perform the division:
$$\dfrac{x^6+3x^5-2x^4+x^2-3x+2}{x-2}.$$
We use synthetic division.
We got:
$$\dfrac{x^6+3x^5-2x^4+x^2-3x+2}{x-2}=x^5+5x^4+8x^3+16x^2+33x+63+\dfrac{128}{x-2}.$$
