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Verified Answer :

JcAlmighty

The answer is C. x+2.


\(\frac{ x^{4} +2 x^{3}-x-2 }{x^{3} -1}\)

Rearrange it:
\(\frac{ x^{4} +2 x^{3}-x-2 }{x^{3} -1}=\frac{ x^{4} -x+2 x^{3}-2 }{x^{3} -1} =\frac{ x*x^{3} -x*1+2*x^{3}-2*1 }{x^{3} -1}= \frac{x( x^{3}-1)+2(x^{3}-1) }{x^{3}-1} = \\ = \frac{(x^{3}-1)(x+2)}{x^{3}-1}\)

x³ - 1 can be cancelled out:
\(\frac{(x^{3}-1)(x+2)}{x^{3}-1} = x+2\)

Answer: x+2. The answer is C.

Step-by-step explanation:

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