Factors Command
From GeoGebra Manual
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- Factors[ <Polynomial> ]
- Yields 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> ]
- Yields 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> ]
- Yields 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> ]
- Yields 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.