Find the HCF of $2 x^{2} - 5 x + 3$ and $6 x^{2} - 5 x + 4$

(2 x - 3)

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(3 x + 4)

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(x + 1) (x + 2)

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Solution

The correct option is B 1
$2 x^{2} - 5 x + 3 = 2 x^{2} - 2 x - 3 x + 3$
$= 2 x (x - 1) - 3 (x - 1)$
$= (x - 1) (2 x - 3)$
and
$6 x^{2} - 5 x - 4 = 6 x^{2} - 8 x + 3 x - 4$
$= 2 x (3 x - 4) + 1 (3 x - 4)$
$= (3 x - 4) (2 x + 1)$
Since no factor is common in two given expressions, 1 will always be a common factor.
$∴ H . C . F . = 1$ .
Option B is correct.

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