# 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

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