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June 5th, 2014, 10:39 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, 10:53 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,329 Thanks: 2452 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 10:56 PM. 
June 6th, 2014, 12:01 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 

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