Answer:
A; x + 1
Step-by-step explanation:
Since the viniculum in a fraction represents division, we can rewrite the expression like this:
[tex]\frac{x^3+1}{x^2-x+1}[/tex]
We can already see that [tex]x^{3} + 1[/tex] could be factored:
Since anything with a "one" as its base will remain one, we can rewrite:
[tex]x^3+1^3[/tex]
Now, we can apply the "sum of cubes" formula:
[tex]\frac{\left(x+1\right)\left(x^2-x+1\right)}{x^2-x+1}[/tex]
Cancelling out!
[tex]x+1[/tex]
Thusly, you are correct and the remainder is [tex]\boxed{x+1{\text{\:or\:A}}}[/tex].
Hope this helps! ((:
