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  "body": "\n## Summary\n\nFactorization of polynomials writes a polynomial as a product of [[irreducible polynomials|03FKX7Z5DC]].\nOver a field the result is unique up to order and constant factors, because $K[x]$ is a [[unique factorisation domain|0W4X9G6263]].\nThe answer depends on the field: $x^2 + 1$ is irreducible over $\\R$ but splits over $\\C$.\nComputing factorizations is a central task of computer algebra, with different methods over finite fields, over $\\Q$ and over number fields.\n\n## Explanations\n\n### L1 human\n\nFactoring a polynomial is like factoring an integer into primes.\nThe irreducible polynomials play the role of the primes.\nFor example, over $\\Q$ one has $x^4 - 1 = (x - 1)(x + 1)(x^2 + 1)$, and none of the three factors can be split further over $\\Q$.\nOver $\\C$ the last factor splits as $(x - i)(x + i)$.\nThe [[definition|EFDBS6ZME8]] states the form of the result.\n",
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