Factors Command

Factors[ <Polynomial> ]

Gives a list of lists of the type {factor, exponent} such that the product of all these factors raised to the power of the corresponding exponents equals the given polynomial. The factors are sorted by degree in ascending order.

Example:

Factors[x^8 - 1] yields {{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}.

Note: Not all of the factors are irreducible over the reals.

Factors[ <Number> ]

Gives matrix of the type \left( \begin{array}{} prime_1 & exponent_1 \\ prime_2 & exponent_2 \\prime_3 & exponent_3 \\ \end{array} \right) such that the product of all these primes raised to the power of the corresponding exponents equals the given number. The primes are sorted in ascending order.

Example:

• Factors[1024] yields ( 2 10 ), since 1024 = 2^{10}.
• Factors[42] yields \left( \begin{array}{} 2 & 1 \\ 3 & 1 \\7 & 1 \\ \end{array} \right) , since 42 = 2^1・3^1・7^1.

Note: See also PrimeFactors Command and Factor Command.

Note: In the CAS View undefined variables can be used as input and the results are returned as proper matrices.

Example: Factors[a^8 - 1] yields \left( \begin{array}{} a - 1 & 1 \\ a +1 & 1 \\a^2 + 1& 1 \\a^4 + 1& 1 \\ \end{array} \right).