Which of the following statement are True? Give reason for your answer . 1. Not every polynomial that is irreducible over Q [ x ] is irreducible over Z [ x ] .

1 Answer
Jim H
Mar 2, 2018

False.

Explanation:

This statement requires that there should be a polynomial that is irreducible over #QQ#, but not irreducible over #ZZ#.

A polynomial that can be factored in #ZZ##[x]# can also be factored in #QQ##[x]#.

That is: every polynomial that is not irreducible over #ZZ# is also not irreducible over #QQ#.

Related questions
Impact of this question
718 views around the world
You can reuse this answer
Creative Commons License