# Query on HCF of polynomials

• In the post https://www.mbatious.com/topic/71/hcf-lcm-concepts-by-gaurav-sharma there was a question:
What is the HCF of x^2 - 5x + 6 and x^2 -7x +12 and the solution was:
x^2 - 5x + 6 = (x-2)(x-3)
x^2 - 7x +12 = (x-3)(x-4)
HCF of [(x-2)(x-3)] and [(x-3)(x-4)] cannot be determined as it depends upon the value of x

My question is that why is HCF not (x-3) (in schools this is what we were taught for HCF of polynomials). Please shed some light.

• there might be common factor in x-2 and x-4 therefore unless x-2 and x-4 are co-primes, x-3 cannot be the HCF

• @naman-jain-0 Can you please explain the same using following question:
find hcf of x^2 + 7x + 6 and x^2 − 5x − 6.
here the answer should be x + 1 (factors are (x + 1)(x + 6) and (x + 1)(x − 6))
Will the concept of checking for co-primes come into play here too ?

• @test1234
If we put x = 1,
x^2 + 7x + 6 = 14 and x^2 − 5x − 6 = -10
Is HCF(14, -10) = 1 + 1 = 2 ?

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