Learning Guide Learning Guide

152 • Chapter 5: Evaluation and Simplification√2 (x 2 + 1) (x + √ 2) (x − √ 2) (x − 1)You can explicitly extend the coefficient field by giving a second argumentto factor.> poly := x^4 - 5*x^2 + 6;poly := x 4 − 5 x 2 + 6> factor( poly );(x 2 − 2) (x 2 − 3)> factor( poly, sqrt(2) );(x 2 − 3) (x + √ 2) (x − √ 2)> factor( poly, { sqrt(2), sqrt(3) } );−(x + √ 2) (x − √ 2) (−x + √ 3) (x + √ 3)You can also specify the extension by using RootOf. Here RootOf(x^2-2)represents any solution to x 2 − 2 = 0, that is either √ 2 or − √ 2.> factor( poly, RootOf(x^2-2) );(x 2 − 3) (x + RootOf(_Z 2 − 2)) (x − RootOf(_Z 2 − 2))For more information on performing calculations in an algebraic numberfield, refer to ?evala.Factoring in Special Domains Use the Factor command to factor anexpression over the integers modulo p for some prime p. The syntax issimilar to that of the Expand command.> Factor( x^2+3*x+3 ) mod 7;(x + 4) (x + 6)The Factor command also allows algebraic field extensions.