Factor

Factor[poly]
factors a polynomial over the integers.
Details and Options

- Factor applies only to the top algebraic level in an expression. You may have to use Map, or apply Factor again, to reach other levels.
- Factor[poly,GaussianIntegers->True] factors allowing Gaussian integer coefficients.
- If any coefficients in poly are complex numbers, factoring is done allowing Gaussian integer coefficients.
- The exponents of variables need not be positive integers. Factor can deal with exponents that are linear combinations of symbolic expressions.
- When given a rational expression, Factor effectively first calls Together, then factors numerator and denominator.
- With the default setting Extension->None, Factor[poly] will treat algebraic number coefficients in poly like independent variables.
- Factor[poly,Extension->Automatic] will extend the domain of coefficients to include any algebraic numbers that appear in poly. »
- Factor automatically threads over lists, as well as equations, inequalities and logic functions.
Examples
open allclose allBasic Examples (3)
Scope (13)
Basic Uses (6)
Advanced Uses (7)
Factor a polynomial over the Gaussian integers:
Factor a polynomial over an algebraic extension:
Factor a polynomial over the integers modulo 3:
Factor polynomials over a finite field:
Factor a polynomial over an extension of a finite field:
A polynomial irreducible over factors after embedding
in a larger field
:
Options (7)
Applications (3)
When modeling behavior with polynomials, it is important to determine when the polynomial evaluates to zero. For example, suppose the cost to produce a video game system is modeled by the following expression:
Also suppose the revenue can be modeled by the equation:
If we wish to know the number of units we must sell before making a profit, we calculate the difference:
Then we solve to find where the profit function is zero using Factor:
This reveals to us there is a zero for profit at :
Find a number which is equal to its square:
Subtract from both sides of the equation:
Use Factor to find when a polynomial is zero:
The only numbers that are equal to their square are thus and
:
Compute the greatest common divisor of two polynomials:
We can see they share a common factor of . Confirm this result using PolynomialGCD:
Properties & Relations (3)
Expand is effectively the inverse of Factor:
FactorList gives a list of factors:
FactorSquareFree only pulls out multiple factors:
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