
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 14th, 2015, 02:37 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, 02:46 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 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, 04:23 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,730 Thanks: 689 
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, 05:04 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,639 Thanks: 2624 Math Focus: Mainly analysis and algebra 
Factorisations are unique up to constant multiples and ordering of terms.

May 15th, 2015, 01:45 AM  #5  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
The key thing is this phrase... Quote:
Quote:
 

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complete, factorization, unique 
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