How to | Factor a Polynomial

Mathematica includes functionality to factor polynomials symbolically.

If you are concerned with factoring a polynomial, Factor is the appropriate command:

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If you would like to specify an extension in which to factor, say one with , use the Extension option:

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If you would like to specify a modulus for the factorization, like 3, use the Modulus option:

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For a polynomial of multiple variables, Factor will still try to decompose it:

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Sometimes, it is more important to find whether the polynomial is irreducible than to try to find its factors explicitly. You can find out with IrreduciblePolynomialQ; for example, this checks if is irreducible:

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To get the largest factor of a collection of polynomials, say , use the PolynomialGCD command:

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A univariate polynomial can always be factored into linear factors by finding all of its roots:

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