# Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division frac{x^{n}-1}{x-1}. Greate a numerical example to test your formula. frac{x^{3}-1}{x-1}

alesterp 2020-12-28 Answered
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $\frac{{x}^{n}-1}{x-1}$.
Greate a numerical example to test your formula.
$\frac{{x}^{3}-1}{x-1}$
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## Expert Answer

Lacey-May Snyder
Answered 2020-12-29 Author has 88 answers
$\frac{{x}^{3}-1}{x-1}$
Here, ${x}^{3}-1$ is the dividend and x - 1 is the divisor.
1 1 0 0 -1
1 1 1
1 1 1 0
So, the quotient is $\left({x}^{2}+x+1\right)$ and the remainder is 0.
Thus, $\frac{{x}^{3}-1}{x-1}={x}^{2}+x+1\left(x\ne 1\right)$.
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