The correct question; What is the remainder when (x3 + 1) is divided by (x² -x + 1)?
By long division method; the remainder when (x³ -1) is divided by (x² - x + 1) is; (x² - x +1)
According to the question;
By long division as in the attached image;
The remainder is; (x² - x +1)
Read more on Polynomial division:
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The remainder when x³ + 1 is divided by x² - x + 1 is; 0
We want to find the remainder when x³ + 1 is divided by x² - x + 1.
This means;
(x³ + 1)/(x² - x + 1)
Now, let us factorize the numerator to make this easy to divide. The factors of x³ + 1 are;
(x + 1) and x² - x + 1. Thus, we now have;
[(x + 1)(x² - x + 1)]/(x² - x + 1)
Looking at both numerator and denominator, x² - x + 1 are common and will cancel out to give;
x + 1.
Thus, the answer to the division of (x³ + 1)/(x² - x + 1) is x + 1 without any remainder.
Read more about division of polynomials at; https://brainly.com/question/17057112
