Can someone help me solve this problem?

Let $F$ a field and $f,g\in R[x]$. Suppose that the set 

$\lbrace{ r(x)f(x) + s(x)g(x) : r(x),s(x)\in F[x] }\rbrace$

is a proper ideal on $F[x]$

It shows that if the degrees of $f$ and $g$ are different, then $f$ and $g$ are not both irreducible.