Question 7044
you need to factorise this: {{{x^4+4x^3+6x^2+8x+8=0}}}. Seeing as how they have asked you, and you know next to nothing about solving {{{x^4}}} polynomials, there has to be a "nice" solution for you. So, lets just re-order the polynomial slightly to:


{{{x^4+6x^2+8 +4x^3+8x=0}}}


Lets treat the first 3 terms as a quadratic and the last 2 terms we will just factorise normally: So


{{{(x^2+2)(x^2+4) + 4x(x^2+2) = 0}}}. Both of these terms have a common term, namely {{{(x^2+2)}}}, so we can factorise again to give:


{{{(x^2+2)(x^2 + 4 + 4x) = 0}}} and the second bracket can be factorised to give


{{{(x^2+2)(x+2)(x+2) = 0}}}


so either {{{x^2+2 = 0}}} or x+2 = 0
so either {{{x^2 = -2}}} or x = -2
so either {{{x = + sqrt(-2)}}} or {{{x = - sqrt(-2)}}} or x = -2

--> {{{x = + sqrt(2)i}}} or {{{x = - sqrt(2)i}}} or x = -2


jon.