Irreduzibles Polynom/X^7129+105X^103+15X+45/Körper/Aufgabe

Wir betrachten das Polynom

P=X^{7129}+105X^{103}+15X+45.

Bestimme für die folgenden Körper ${}K$ , ob ${}P$ irreduzibel in ${}K[X]$ ist.

a) ${}K=\mathbb {Q}$ .

b) ${}K=\mathbb {R}$ .

c) ${}K=\mathbb {Z} /(2)$ .

d)

{}K=\mathbb {Q} [T]/(T^{7129}+105T^{103}+15T+45)

.

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