
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
May 14th, 2015, 03:37 PM  #1 
Newbie Joined: Dec 2013 Posts: 28 Thanks: 0  Is a complete factorization unique?
Say we are asked to factor a polynomial completely over the integers Is there more than one possible result? for example (3x+3) factors completely as 3(x+1) but if I give as an answer (3)(1)(x+1), is it wrong? 
May 14th, 2015, 03:46 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond 
I wouldn't say that it's wrong, but I'd say that it's trivial.

May 14th, 2015, 05:23 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 658 
When describing unique factorization, factors of 1 don't count. Along the same lines, changing signs of two factors is also not relevant.

May 14th, 2015, 06:04 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra 
Factorisations are unique up to constant multiples and ordering of terms.

May 15th, 2015, 02:45 AM  #5  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,134 Thanks: 720 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
The key thing is this phrase... Quote:
Quote:
 

Tags 
complete, factorization, unique 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
unique factorization domain, zero of a polynomial , proof  rayman  Abstract Algebra  2  October 19th, 2012 07:38 AM 
Unique factorization domain  Lokokatz3nkl0  Number Theory  1  September 10th, 2012 06:12 AM 
Proving unique factorization for polynomials  squelchy451  Number Theory  1  July 3rd, 2010 04:42 AM 
Unique factorization Domain  Ann  Abstract Algebra  0  November 25th, 2006 06:41 PM 
Unique factorization Domain  Ann  New Users  0  December 31st, 1969 04:00 PM 