April 25th, 2017, 01:01 PM  #1 
Newbie Joined: Apr 2017 From: United Kingdom Posts: 1 Thanks: 0  Homework Problem
Hello, I am a bit stuck on this question and can't start it.. Any help is very welcome, thanks in advance. Q: In the ring R=ℚ[x]/(x^5) find the inverse element for (12(x^2)+x^3). 
April 25th, 2017, 03:21 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,524 Thanks: 642 
Q[x]/x^5, if I understand your notation, correctly, can be interpreted as the field of all polynomials, with rational coefficients, of degree 5 of less with multiplication defined as regular polynomial multiplication except that we drop all powers of x larger than 4. To find the multiplicative inverse of 1+ 2x^2+ x^3, we look for ax^4+ bx^3+ cx^2+ dx+ e such that this multiplication gives 1. That is, we look at (x^3+ 2x^2+ 0x+1)(ax^4+ bx^3+ cx^2+ dx+ e)= ax^7+ (2a+ b)x^6+ (2b+ a)x^5+ (a+ 2c+ d)x^4+(c+2e)x^2+ dx+ e= (a+ 2c+ d)x^4+ (b+ 2d+ e)x^3+(c+2e)x^2+ dx+ e since we drop the x^7, x^6, and x^5 terms. We want that to be equal to 1 so we must have a+ 2c+ d= 0, b+ 2d+ e= 0, c+ 2e= 0, d= 0, and e= 1. Solve those five equations for a, b, c, d, and e. 

Tags 
homework, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Trigonometry Homework problem.  TrimHonduras  Trigonometry  1  July 21st, 2013 06:40 PM 
I need help with my homework!  gasteven  Algebra  2  February 14th, 2013 10:56 AM 
homework help  andi7  Algebra  1  October 24th, 2009 04:17 AM 
homework help!  andi7  Algebra  6  March 13th, 2009 10:55 AM 
gcd homework problem  Jamers328  Number Theory  3  September 27th, 2007 08:00 AM 