Question

find the LCM and HCF of x^3-8 and x^2-4​

Answer 1

Answer:

Factorise all the polynomials

3x

2

−6x=3x(x−2)

x

2

−4x+4=(x−2)(x−2)

x

2

+x−6=(x−2)(x+3)

The least common multiple for the first two polynomials is 3x(x−2)

2

The LCM of three polynomials is LCM of 3x(x−2)

2

and (x−2)(x−3)

⇒LCM=3x(x−2

2

)(x+3)

The highest common factor of first two polynomials is (x−2)

The HCF of all the three polynomials is HCF of (x−2) and (x−2)(x−3)

⇒HCF=(x−2)