One of the factor of $x^{2} - 1$ is $(x - 1)$ , then the other factor is_______

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Solution

$x^{2} - 1$ is of the form $a^{2} - b^{2}$
$∴ x^{2} - 1 = (x - 1) (x + 1)$ where $a^{2} - b^{2} = (a - b) (a + b)$
Hence factors of $x^{2} - 1$ is $(x - 1) (x + 1)$
If $(x - 1)$ is one factor of $x^{2} - 1$ then the other factor is $(x + 1)$

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