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

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Solution

Given polynomial is $x^{3} - 3 x^{2} + 3 x - 2$ .
To find out: Whether $x^{2} - x + 1$ is a factor of the given polynomial or not.

$x^{2} - x + 1$ will be a factor of $x^{3} - 3 x^{2} + 3 x - 2$ when the remainder is zero.

Dividing $x^{3} - 3 x^{2} + 3 x - 2$ by $x^{2} - x + 1$ , as shown in the figure. We get:
Quotient as $x - 2$ .
and Remainder as $0$ .

Since the remainder is $0$ , $x^{2} - x + 1$ is a factor of $x^{3} - 3 x^{2} + 3 x - 2$ .

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