Existence of non-zero subspace given linear map

Question

Let $V$ be a real vector space over $\mathbb{R}$ with $\dim(V) \geq 3$. Show that $\exists W \subset V : W \ne V, W \ne \{0\}$ and $T(W) \subset W$ with $T \in End_{\mathbb{R}}(V)$ arbitrary. The solution considers $V$ as a $\mathbb{R}[T]$ module, with the operation of $f(T)\cdot v = f(T(v)) \in V$. They then show $V$ cannot be a simple module because if it were, then it is isomorphic to $\mathbb{R}[T] / (f(T))$, where $f(T)$ has degree at least $3$ and is an irreducible polynomial, which they state cannot exist. Can someone give me a reason why a degree at least $3$ irreducible polynomial cannot exist in $\mathbb{R}[T]$?