Why is HCF of $x^2-1$ and $x-1$ is $x-1$, "why can't it be $1-x$?" I've been to different site and tried to find it using Mathematica also, but everywhere they put the answer $x-1$ before me.
I even tried to find for $1-x^2$ and $1-x$, then also I got the  answer $x-1$.
Can anyone explain please!

A $\gcd$ (or $\operatorname{hcf}$) is only defined up to associates in the respective ring. For real polynomials, the usual convention is to define the $\gcd$ to be the monic polynomial among those, since the units are the (non-zero) constant polynomials.
