Split polynomial

Remarks

Then $c$ is the leading coefficient of $f$, $n = \deg f$, and $a_1, \dots, a_n$ are the roots of $f$, not necessarily distinct. The polynomial $x^2 - 2$ splits over $\mathbb{R}$, but not over $\mathbb{Q}$. The polynomial $x^2 + 1$ splits over $\mathbb{C}$, but not over $\mathbb{R}$. Over an algebraically closed field, every nonzero polynomial splits.