Polynomial ring/Field/One variable/Field extension/Divisor relation/Exercise

Let ${}K$ be a field, and let ${}K[X]$ be the polynomial ring over ${}K$. Let ${}F,G\in K[X]$ be polynomials. Let ${}K\subseteq L$ be a field extension. Show that ${}F$ is a divisor of ${}G$ in ${}K[X]$ if and only if ${}F$ is a divisor of ${}G$ in ${}L[X]$.

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