You can put this solution on YOUR website! you take 27x^3 + 8 and you make it 27x^3 + 0x^2 + 0x + 8 by filling in the terms with missing degrees, such as x^2 and x.
you then divide this by 3x + 2 by following the recommended procedure for algebra long division.
your answer will be 9x^2 - 6x + 4
you then multiply that by (3x + 2) to get back to the original dividend of 27x^3 + 8.
the procedure for algebraic long division can be found here.
for purposes of this problem, i think you can skip the simplification part and just go to the long division part and then to the examples part.
i sent you directly to the long division part.
any questions after reading the tutorial, send me an email and i'll explain as best i can.