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Method of Finding HCF

If px=4 x 2...

Question

If $p (x) = 4 x^{2} - 4 x - 80$ and $q (x) = 8 x^{2} + 24 x - 32$ , find their HCF.

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Solution

We have
$p (x) = 4 x^{2} - 4 x - 80 = 4 (4 x^{2} - 4 x - 80 - x - 20) = 4 (4 x^{2} - 4 x - 80 - 5 x + 4 x - 20)$
$= 4 (x (x - 5) + 4 (x - 5)) = 4 (x - 5) (x + 4)$ .
Similarly,
$q (x) = 84 x^{2} - 4 x - 80 + 24 - 32 = 8 (4 x^{2} - 4 x - 80 + 3 x - 4)$
$= 8 (4 x^{2} - 4 x - 80 + 4 x - x - 4) = 8 (x (x + 4) - (x + 4))$
$4 \times 2 (x - 1) (x + 4)$
Here we see that $4$ and $x + 4$ are two common factors between $p (x)$ and $q (x)$ . Their product $4 (x + 4)$ is HCF of $p (x)$ and $q (x)$ .

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