Question

The GCD and LCM of two polynomials are x+1 and x^6-1 respectively. If one of the polynomials is x^3+1 find the other.

Answer 1

Answer:

Given GCD =x+1 and LCM =x

6

−1

Let f(x)=x

3

+1.

We known that LCM×GCD=f(x)×g(x)

→g(x)=

f(x)

LCM×GCD

=

x

3

+1

(x

6

−1)(x+1)

x

3

+1

(x

3

+1)(x

3

−1)(x+1)

=(x

3

−1)(x+1)

Hence, g(x)=(x

3

−1)(x+1).