Question

Find the G.C.D. and L.C.M. of 8(x³ -x² +x) and 28(x³ + 1)​

Answer 1

Answer:

The relation between H.C.F. and L.C.M. of two polynomials is the product of the two polynomials is equal to the product of their H.C.F. and L.C.M.

If p(x) and q(x) are two polynomials, then p(x) ∙ q(x) = {H.C.F. of p(x) and q(x)} x {L.C.M. of p(x) and q(x)}.

1. Find the H.C.F. and L.C.M. of the expressions a2 – 12a + 35 and a2 – 8a + 7 by factorization.

Solution:

First expression = a2 – 12a + 35

= a2 – 7a – 5a + 35

= a(a – 7) – 5(a – 7)

= (a – 7) (a – 5)

Second expression = a2 – 8a + 7

= a2 – 7a – a + 7

= a(a – 7) – 1(a – 7)

= (a – 7) (a – 1)

Therefore, the H.C.F. = (a – 7) and L.C.M. = (a – 7) (a – 5) (a – 1)

Note:

(i) The product of the two expressions is equal to the product of their factors.

(ii) The product of the two expressions is equal to the product of their H.C.F. and L.C.M.