Question

Find the
HCF
and LCM of
of f(x) = 4 (x³+ x²+x) and
g(x) = 24 (x³-1)​

Answer 1

Answer:

x

3

−1=x

3

−1

3

=(x−1)(x

2

+x+1)

x

4

+x

2

+1=(x

4

+2x

2

+1)−x

2

=(x

2

+1)

2

−(x)

2

=(x

2

+1+x)(x

2

+1−x)

=(x

2

+x+1)(x

2

−x+1)

Hence, H.C.F. of x

3

−1 and x

4

+x

2

+1 is x

2

+x+1.

and the LCM

x

3

+x

2

+x+1=(x+1)(x

2

+1) also x

3

−x

2

+x−1=(x−1)(x

2

+1)

∴L.C.M.=(x

2

+1).