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!

You can define a HCF of polynomials $f$ and $g$ to be a polynomial $h$ with the two properties


*

*$h\mid f$ and $h\mid g$;

*if $p\mid f$ and $p\mid g$ then $p\mid h$.


In this case $x-1$ and $1-x$ are both correct, and in fact so is any non-zero constant times $x-1$.
However some people add a third property to the definition,


*

*$h$ is monic, that is, the leading coefficient is $1$.


In this case $x-1$ is the only correct answer.
