Use the Simplify > Factor command or press Ctrl+F to factor the currently highlighted expression or subexpression with respect to some or all of its variables.  (Note that the Factoring FunctionsFactoring_Functions can also be used to factor an expression.)  If only a subexpression is highlighted, the result is a copy of the whole expression with just the subexpression factored.  This command displays a dialog box with fields for specifying the expression factoring type and the factor variables.


The Expression Factoring Type field allows you to specify the amount and kind of factoring to use on the expression:

•        Prime number decomposition to factor a number and the numeric coefficients of the terms of a polynomial.

•        Trivial content to place an expression over a common denominator and factor out the trivial content of the terms of the expression.

•        Squarefree polynomial to factor a polynomial to factors that are free of perfect powers.

•        Rational polynomial to factor a polynomial as much as possible without introducing fractional powers or complex numbers.

•        Radical polynomial to factor a polynomial as much as possible without introducing complex factors.

•        Complex polynomial to factor a polynomial as much as possible.

•        Turing LU matrix to factor a matrix into its five Turing factors which includes its LU factors and its reduced row echelon form.

•        Gram-Schmidt QR matrix to factor a matrix into its QR factors.


Univariate polynomials are factored with respect to its variable.  Multivariate polynomials can be factored with respect to some or all of its variables.  The Factor Variables field displays a list of all the variables in the highlighted expression or subexpression, and allows you to select the desired factorization variables.  Click on the desired primary factorization variable, then click on the secondary factorization variable, etc.  These factorization variables temporarily override the ordering specified by the variable order listed on the Output tab of the Options > Mode Settings command3L4YH.


The Simplify > Factor command (when not introducing fractional powers) and the Simplify > Basic commandBQ.NIL both transform an expression into a sufficiently simple formSufficiently_simple_form.  However, the Simplify > Basic command is usually faster and yields a result more similar to the original expression.


The Simplify > Factor command can also be used to transform Boolean expressions into conjunctive normal form (see Boolean FunctionsBoolean_Functions for details).


For more about factoring see Factoring NumbersFactoring_Numbers, Factoring PolynomialsFactoring_Polynomials, and Factoring MatricesFactoring_Matrices.


Other Simplify commandsSimplify_commands 

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