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Method of Finding HCF

Find the H.C....

Question

Find the H.C.F of $(x + 1) (x^{2} - 4)$ and $(x^{2} - 1) (x - 2)$

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Solution

Let
$p (x) = (x + 1) (x^{2} - 4) = (x + 1) (x + 2) (x - 2)$
and
$q (x) = (x^{2} - 1) (x - 2) = (x + 1) (x - 1) (x - 2)$

The common factor of $p (x)$ and $q (x)$ is $= (x + 1) (x - 2)$

$∴$ H.C.F of $p (x)$ and $q (x)$ $= (x + 1) (x - 2)$

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