If the LCM of $f (x)$ and $g (x)$ is $6 x^{2} + 13 x + 6$ and their HCF is a linear polynomial. Find the possible HCF of $f (x)$ and $g (x)$ .

2 x - 3

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3 x + 2

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3 x - 2

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3 x + 4

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Solution

The correct option is B $3 x + 2$
We know that HCF of two polynomials is a factor of their LCM.
GIven, LCM $= 6 x^{2} + 13 x + 6 = 6 x^{2} + 4 x + 9 x + 6 = 2 x (3 x + 2) + 3 (3 x + 2) = (2 x + 3) (3 x + 2)$
Thus, HCF of the polynomials can be $2 x + 3$ or $3 x + 2$

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