Answer: C. x-2
Step-by-step explanation:
We have the following expression:
[tex]\frac{x^{4} -2x^{3} +x-2}{x^{3}+1}[/tex]
Factoring in the numerator:
[tex]\frac{x(x^{3}+1)-2(x^{3}+1)}{x^{3}+1}[/tex]
Factoring again in the numerator with common factor [tex]x^{3}+1[/tex]:
[tex]\frac{(x^{3}+1)(x-2)}{x^{3}+1}[/tex]
Simplifying:
[tex]x-2[/tex]
Hence, the correct option is C. x-2
