$f,g\in P$ is a set of polynomials with coefficients in R. $fTg$ if $f-g=c$ for $\exists c\in R$. Show T is an equivalence relation on P

Question

$f,g\in P$ is a set of polynomials with coefficients in R. $fTg$ if $f-g=c$ for $\exists c\in R$. Show T is an equivalence relation on P

I'm assuming we can show it's symmetric because if f-g=c then g-f=-c, and since c is in R then -c is in R as well.

Then f-f=0 which is in R, but I don't know how to show it's transitive

Answer 1

$f-g=c$ and $g-h=d$ implies $f-h =c+d$ by addition.