If you have a new account but are having problems posting or verifying your account, please email us on hello@boards.ie for help. Thanks :)

Hello all! Please ensure that you are posting a new thread or question in the appropriate forum. The Feedback forum is overwhelmed with questions that are having to be moved elsewhere. If you need help to verify your account contact hello@boards.ie

Hi there,
There is an issue with role permissions that is being worked on at the moment.
If you are having trouble with access or permissions on regional forums please post here to get access: https://www.boards.ie/discussion/2058365403/you-do-not-have-permission-for-that#latest

Find the irreducible factors.

franksarms · 2013-04-16 13:55:38

This a question taken from a first year Honours Maths Paper in University : Find the irreducible factors of x^3 + 6x^2 + 3x + 3 in Z13[x]. (Integers modulo 13) Don't have a notion of how to solve it so much thanks for any help!!

16-04-2013 1:55pm

#1

franksarms

Registered Users, Registered Users 2 Posts: 12 ✭

Join Date: April 2012

Posts: 7

This a question taken from a first year Honours Maths Paper in University :
Find the irreducible factors of
x^3 + 6x^2 + 3x + 3 in Z13[x]. (Integers modulo 13)

Don't have a notion of how to solve it so much thanks for any help!!

0

Comments

#2 16-04-2013 10:55pm

CJC86

Registered Users, Registered Users 2 Posts: 360 ✭✭

Join Date: March 2010

Posts: 347

An important point to note is that the factor theorem holds for all fields, not just the reals/complex numbers. Hence, you should plug in values 0,...,12 for x, and note that any result which is a multiple of 13 is 0 in Z13[x]; then, if k solves f(x)=0, then (x-k) divides f(x).

0