Polynomial ring/Field/Zero/Linear factor/Fact
Let be a field and let be the polynomial ring over . Let be a polynomial and .
Then is a
zero
of if and only if is a multiple of the linear polynomial .
Let 
![{\displaystyle {}K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7861df9df3d7463835d927c4d0d4c27f5e2f8416)
![{\displaystyle {}P\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4692e3ffcbd66e900f8975113ff3f32f1cabc21a)
is a
zero
of
if and only if is a multiple of the linear polynomial 
.