Cubic polynomials

Algebra Level 5

Let $f (x), g(x)$ be two monic cubic polynomials and $r$ a real number.

$f (x)$ has roots $r+1, r+7$ only.

$g (x)$ has roots $r+3, r+9$ only.

Suppose $f (x)-g (x)=r$ for all $x$ . Find $r$ .

This problem is part of the set ... and polynomials