Determine whether $(x + 1)$ is a factor of $x^{3} + x^{2} + x + 1$
Write 1 if true and 0 if false

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Solution

$x^{3} + x^{2} + x + 1$
Let $p (x) = x^{3} + x^{2} + x + 1$
The zero of $x + 1$ is $- 1$
$p (- 1) = (- 1)^{3} + (- 1)^{2} + (- 1) + 1$
$= - 1 + 1 - 1 + 1 = 0$
$∴ (x + 1)$ is a factor of $x^{3} + x^{2} + x + 1$

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