Question

Factorize :x^4 - 14 + 1​

Answer 1

Step-by-step explanation:

Well, I read this question first wrongly, because the reader is about complex analysis, I did it for C first.

I got. x4+1=(x−eπi/4)(x−e3πi/4)(x−e5πi/4)(x−e7πi/4).

My teacher told me that there is very smart way to do this for R that we already learned. But I only can think of trial and error kind of methods.Group each complex root α with α¯:

(x−α)(x−α¯)=x2−(α+α¯)x+αα¯∈R[x].