Factoring Expressions

To factor an expression for an integer or rational function, place the cursor at the end of the expression and either:

Then press [Enter].

The "factor" command factors an integer into a product of primes, and factors a polynomial or rational function into a product of lower-order polynomials or rational functions.

To perform a more complete factorization, type a comma after "factor," and then type a comma-separated list of radicals occurring in the roots of the expression in the placeholder.

Examples:

100 factor → 22 · 52

x2 − 7x + 12 factor → (x − 3) · (x − 4)

Factoring Polynomials With Irrational Roots

By default, Mathcad factors a polynomial with rational coefficients into a product of lower-order polynomials with rational coefficients, if possible. For a polynomial such as x2 − 2, which cannot be factored over the rational numbers because its roots are irrational, Mathcad returns the polynomial unchanged.

x2 − 2 factor → x2 − 2

To factor the polynomial further x2 − 2, type one of its roots, Square root of 2, after the keyword "factor."

x squared minus 2 factored

This factors x2 − 2 into a product of polynomials whose coefficients involve Square root of 2.

Note: In general, Mathcad factors a polynomial over the field of numbers generated by its coefficients. For example, if Square root of 2 appears among the coefficients, Mathcad factors the polynomial into terms containing Square root of 2.

To factor a polynomial with complex roots, insert the complex number i after "factor."

x2 + 1 factor, i → (x − i) · (x + i)

If you don't know the roots of the polynomial, solve it first using the keyword "solve."

roots of x squared minus x minus 1

Then copy and paste the radical appearing in the roots, or either one of the roots themselves, into the placeholder after "solve."

x squared minus x minus 1 factored

The following link opens a Mathcad worksheet containing live examples of "factor."

QuickSheet - Factoring and Expanding Expressions

Note:

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