Question

Pn= x^n -1. Descompuneti P12 in factori ireductibili peste R

Answer 1

Răspuns:

(x-1)(x+1) (x²+x+1)(x²-x+1) (x^6+1)

Explicație pas cu pas:

x^12-1=(x^6-1) (x^6+1) =(x³-1)(x³+1)(x^6+1)=

=(x-1)(x+1) (x²+x+1)(x²-x+1) (x^6+1)

Answer 2

$\it P_{12}=x^{12}-1=(x^6)^2-1^2=(x^6-1)(x^6+1)=[(x^3)^2-1][(x^2)^3+1]=\\ \\ =(x^3-1)(x^3+1)(x^2+1)(x^4+x^2+1)=\\ \\ =(x-1)(x^2+x+1)(x+1)(x^2-x+1)(x^2+1)(x^4+x^2+1)$