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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: 7,675 Thanks: 2655 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. Thanks from mikeinitaly 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 Tags factoring, polynomials Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post J.Xavier Algebra 1 May 5th, 2013 04:29 PM IDoNotLikeMath Algebra 4 July 10th, 2012 08:59 PM Pumpkin99 Algebra 1 October 6th, 2011 07:58 PM cafegurl Algebra 2 September 26th, 2010 01:55 PM BrandonFlorida Real Analysis 3 May 26th, 2007 11:14 AM

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