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hodyreva [135]
3 years ago
14

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

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0

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 "<em>one</em><em>" </em>as its base will remain one, we can rewrite:

x^3+1^3

Now, we can apply the "<em>sum of cubes</em>" 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! ((:

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