polynomials 题目

chriswong89

题目是   x^5 + x^3 + x

Factorise the polynomials!!!!

答案是   x(1- x + x^2)(1 + x + x^2)

请问如何得到这答案？？？

kenny56

x^5 + x^3 + x
= x(x^4+x^2+1)
=x(x^2+2x^2+1-x^2)
=x((x^2+1)^2-x^2)
=x(x^2+x+1)(x^2+1-x)

[ 本帖最后由 kenny56 于 29-7-2007 10:18 AM 编辑 ]

chriswong89

谢谢您的帮忙！！！我明白了！！！

xanadunext

x^5 + x^3 + x

=x(x^4 + x^2 + 1)

=x . [(x^2)^3 - 1]/(x^2 - 1)     use geometric progression formula

=x . [(x^6 - 1)/(x^2 - 1)]

=x . (x^3 - 1)/(x - 1) . (x^3 + 1)/(x + 1)

=x . (x^3 - 1)/(x - 1) . (- x^3 - 1)/(- x - 1)

=x . (x^2 + x + 1) . (x^2 - x + 1)