Find the HCF $h (x)$ of the following polynomials and using HCF $h (x)$ , find the LCM $m (x)$ , the polynomials are: $3 x^{2} + 5 x - 2, 3 x^{2} - 7 x + 2$

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Solution

Let $p (x) = 3 x^{2} + 5 x - 2$ and $q (x) = 3 x^{2} - 7 x + 2$
$p (x) = 3 x^{2} + 5 x - 2$
$= 3 x^{2} + 6 x - x - 2$
$= 3 x (x + 2) - (x + 2)$
$⟹ p (x) = (3 x - 1) (x + 2)$ ...... $(i)$
$q (x) = 3 x^{2} - 7 x + 2$
$= 3 x^{2} - 6 x - x + 2$
$= 3 x (x - 2) - (x - 2)$
$⟹ q (x) = (3 x - 1) (x - 2)$ ....... $(i i)$
HCF $h (x) = 3 x - 1$
LCM $m (x) = (3 x - 1) (x + 2) (x - 2) = (3 x - 1) (x^{2} - 4)$

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