The answer is C. x+2.
[tex] \frac{ x^{4} +2 x^{3}-x-2 }{x^{3} -1} [/tex]
Rearrange it:
[tex]\frac{ x^{4} +2 x^{3}-x-2 }{x^{3} -1}=\frac{ x^{4} -x+2 x^{3}-2 }{x^{3} -1} =\frac{ x*x^{3} -x*1+2*x^{3}-2*1 }{x^{3} -1}= \frac{x( x^{3}-1)+2(x^{3}-1) }{x^{3}-1} = \\
= \frac{(x^{3}-1)(x+2)}{x^{3}-1} [/tex]
x³ - 1 can be cancelled out:
[tex]\frac{(x^{3}-1)(x+2)}{x^{3}-1} = x+2[/tex]
