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Factorisation by Common Factors

Check x2-x+...

Question

Check $x^{2} - x + 1$ is a factor of $x^{3} - 3 x^{2} - 3 x - 2$

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Solution

We divide $x^{3} - 3 x^{2} - 3 x - 2$ by $x^{2} - x + 1$ and if we get the remainder as $0$ then it means that $x^{2} - x + 1$ is a factor of $x^{3} - 3 x^{2} - 3 x - 2$ .

From the above division, we have the quotient $x - 2$ and the remainder is $0$ .

Hence, $x^{2} - x + 1$ is a factor of $x^{3} - 3 x^{2} - 3 x - 2$ .

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