Wir betrachten das Polynom
Bestimme für die folgenden Körper K {\displaystyle {}K} , ob P {\displaystyle {}P} irreduzibel in K [ X ] {\displaystyle {}K[X]} ist.
a) K = Q {\displaystyle {}K=\mathbb {Q} } .
b) K = R {\displaystyle {}K=\mathbb {R} } .
c) K = Z / ( 2 ) {\displaystyle {}K=\mathbb {Z} /(2)} .
d) K = Q [ T ] / ( T 7129 + 105 T 103 + 15 T + 45 ) {\displaystyle {}K=\mathbb {Q} [T]/(T^{7129}+105T^{103}+15T+45)} .
, ob 
irreduzibel in ![{\displaystyle {}K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7861df9df3d7463835d927c4d0d4c27f5e2f8416)
ist.
.
.
.
![{\displaystyle {}K=\mathbb {Q} [T]/(T^{7129}+105T^{103}+15T+45)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a181d9be67a5dac6e2a44189c27721cbcac71977)
.
