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Factor Theorem

Prove that ...

Question

Prove that $x - 1$ is a factor of $x^{3} - 6 x^{2} + 1 x - 6$ .

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Solution

Let $p (x) = x^{3} - 6 x^{2} + 11 x - 6$ .
$p (1) = 1 - 6 + 11 - 6 = 0$ . (note that sum of the coefficients is 0)
Thus, $(x - 1)$ is a factor of $p (x)$ .

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