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 descending order.

Example:

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

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

Factors[ <Number> ]

Gives a list of lists of the type {prime, exponent} 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 {{2, 1}, {3, 1}, {7, 1}}, since 42 = 2^1 * 3^1 * 7^1.

Note: See also PrimeFactors Command and Factor Command.

CAS Syntax

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 descending order.

Example:

Factors[x^8 - 1] yields {{x^4 + 1, 1}, {x^2 + 1, 1}, {x + 1, 1}, {x - 1, 1}}, displayed as \begin{pmatrix} x^4+1&1\\ x^2+1&1\\ x+1&1\\ x-1&1

\end{pmatrix}.

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

Factors[ <Number> ]

Gives a list of lists of the type {prime, exponent} 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}}, displayed as \begin{pmatrix} 2&10 \end{pmatrix}, since 1024 = 2^{10}.

  • Factors[42] yields {{2, 1}, {3, 1}, {7, 1}}, displayed as \begin{pmatrix} 2&1\\ 3&1\\ 7&1
    \end{pmatrix}, since 42 = 2^1 * 3^1 * 7^1.

Note: See also PrimeFactors Command and Factor Command.