
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 5th, 2014, 11:39 PM  #1 
Senior Member Joined: Oct 2012 From: Live and work in Saudi but from Italy (British national) Posts: 103 Thanks: 2 Math Focus: Hoping to do something in the future.  Factoring Polynomials
Hi all, I've just watched a video on youtube Algebra 2  Dividing Polynomials  YouTube where x^2+6x+5 / x+1 was factored. His result was (x+5)(x+1) / (x+1) Why didn't he factor / consider the 6x ? I admit that I havent started to learn how to factor polynomials and my question is purely out of curiosity. Thanks Mike 
June 5th, 2014, 11:53 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra 
For $x^2 +bx +c$ there are two roots $x = r_1$ and $x = r_2$ so that the equation is $$(x  r_1)(x  r_2)$$ If we multiply out the brackets we get $$x^2  (r_1 + r_2)x + r_1 r_2$$ So $c$ is the product of the two roots and $b$ is minus the sum of the two roots. In the case of your example, the only pair of integers that multiply to make 5 are 1 and 5, so those are the roots to try. Any quadratic $x^2 + bx + c$ where $b$ and $c$ are both integers can have two integer roots or two irrational roots or no real roots at all. Last edited by v8archie; June 5th, 2014 at 11:56 PM. 
June 6th, 2014, 01:01 AM  #3 
Senior Member Joined: Oct 2012 From: Live and work in Saudi but from Italy (British national) Posts: 103 Thanks: 2 Math Focus: Hoping to do something in the future. 
Thanks for that its always helpful to know why! Thanks Mike 

Tags 
factoring, polynomials 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
help factoring polynomials  J.Xavier  Algebra  1  May 5th, 2013 05:29 PM 
Factoring Polynomials  IDoNotLikeMath  Algebra  4  July 10th, 2012 09:59 PM 
Factoring Polynomials  Pumpkin99  Algebra  1  October 6th, 2011 08:58 PM 
Factoring Polynomials:  cafegurl  Algebra  2  September 26th, 2010 02:55 PM 
Factoring Polynomials  BrandonFlorida  Real Analysis  3  May 26th, 2007 12:14 PM 