Question

The LCM and GCD of two polynomials are 3p2 – 8p + 5 and 6p2 + 7p – 5. Find the other polynomial when one of the polynomials is 9p2 – 25

Answer 1

given,

LCM = 3p^2 - 8p + 5

= 3p^2 - 5p - 3p + 5

= p(3p - 5) - 1(3p - 5)

= (3p - 5)(p.- 1)

HCF = 6p^2 + 7p - 5

= 6p^2 + 10p - 3p - 5

= 2p(3p + 5) - 1(3p + 5)

= (3p + 5)(2p - 1)

one polynomial is

9p^2 - 25

= (3p)^2 - 5^2

= (3p - 5)(3p + 5)

the other polynomial would be

= (LCM x HCF)/ one no.

= (3p-5)(p-1)(3p+5)(2p-1) / (3p-5)(3p+5)

= (p-1)(2p-1)

= 2p^2 - 2p - p + 1

= 2p^2 - 3p + 1

=