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Factor Theorem

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Question

What is factor of $m^{3} - m^{2} - m + 4$

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Solution

$m^{3} - m^{2} - m + 4$
$\Rightarrow m^{2} (m - 1) - 1 (m - 1) + 3$
$\Rightarrow (m^{2} - 1) (m - 1) + 3$
$\Rightarrow (m + 1) (m - 1) (m - 1) + 3$
$\Rightarrow (m + 1) (m - 1)^{2} + 3$

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