Using Factor Theorem, show that $(x - 3)$ is a factor of $x^{3} - 3 x^{2} + 4 x - 12.$

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Solution

Given: $x^{3} - 3 x^{2} + 4 x - 12$
$= x^{2} (x - 3) + 4 (x - 3)$
$= (x^{2} + 4) (x - 3)$
$∴ (x - 3)$ is a factor of $x^{3} - 3 x^{2} + 4 x - 12$ .

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