Question

What is the remainder when (x^3+1) is divided by (x^2-x+1)?

Answer 1

Answer:

A; x + 1

Step-by-step explanation:

Since the viniculum in a fraction represents division, we can rewrite the expression like this:

$\frac{x^3+1}{x^2-x+1}$

We can already see that $x^{3} + 1$ could be factored:

Since anything with a "one" as its base will remain one, we can rewrite:

$x^3+1^3$

Now, we can apply the "sum of cubes" formula:

$\frac{\left(x+1\right)\left(x^2-x+1\right)}{x^2-x+1}$

Cancelling out!

$x+1$

Thusly, you are correct and the remainder is $\boxed{x+1{\text{\:or\:A}}}$.

Hope this helps! ((: