Field Extensions, Subfield

Question

Let $F$ be a subfield of a field $K$ and let $t \in K$

Let $t$ be algebraic of degree $n>1$ over $F$. Prove that $[K:F] \ge n$

Clearly there exists a polynomial $P(x)$ such that $P(t)=a_0+a_1t+a_2t^2+\dots+a_nt^n=0$, but I'm not sure how to show the dimension of $K$ as a vector space over $F$ is $\ge n$.

Answer 1

Hint: If $t\in K$ is algebraic of degree $n$ over $F$, then $1$, $t$, $t^2$, ..., $t^{n-1}$ are linearly independent over $F$.