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.

Factors(x^8 - 1) yields {{x - 1, 1}, {x + 1, 1}, {x^2 + 1, 1}, {x^4 + 1, 1}}.

Not all of the factors are irreducible over the reals.

Factors( <Number> ): Gives matrix of the type \(\left( \begin{array}{ll} prime_1 & exponent_1 \\ prime_2 & exponent_2 \\prime_3 & exponent_3 \\ \end{array} \right) \) 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.

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

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

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