Question

find the h.c.f of $x^3+1 & x^4+x^2+1$​

Answer 1

$x^3+1=x^3+1^3\\=(x+1)(x^2-x+1)\\and=x^4+x^2+1\\=(x^2)^2+2x^2+1-x^2\\=(x^2+1)^2-(x)^2\\=(x^2+x+1)(x^2-x+1)\\H.C.F= (x^2-x+1)$