Question

Find hcf,lcm of x^4-1,x^4-x^3+x-1

Answer 1

Hi,

Explanation:

`x^4-1=(x^2+1)(x+1)(x-1)\\\\x^4-x^3+x-1=x^3(x-1)+(x-1)=(x-1)(x^3+1)=(x-1)(x+1)(x^2-x+1)\\\\hcf(x^4-1,x^4-x^3+x-1)=(x-1)(x+1)\\\\lcm(x^4-1,x^4-x^3+x-1)=(x-1)(x+1)(x^2+1)(x^2-x+1)`