The splitting field of a polynomial with coefficients in a field, $F$, is the smallest field extension to $F$ such that the polynomial decomposes into linear factors. Often used with (galois-theory).
Questions tagged [splitting-field]
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Does $x^3-x+3$ have any roots in $\mathbb{F}_5$?
Does $x^3-x+3$ have any roots in $\mathbb{F}_5$? I don't think it does but the only way I know to check is by trial and error and there's only so many factors I can try before my hand cramps up.
Tim
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