Why is 3 a non-unit in Z[x]
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Why is 3 a non-unit in Z[x]

[From: ] [author: ] [Date: 11-05-14] [Hit: ]
3 is not a unit in Z[x].I hope this helps!......
Suppose that 3 is a unit.

Then 3 * p(x) = 1 for some p(x) in Z[x].

By comparing degrees,
deg (3 p(x)) = deg 3 + deg p(x) = deg 1
==> 0 + deg p(x) = 0
==> deg p(x) = 0.

However, that would imply that p(x) = 1/3, which is not an integer.
Hence, 3 is not a unit in Z[x].

I hope this helps!
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