My Math Forum grouping x^3-x^2+x-1

 Algebra Pre-Algebra and Basic Algebra Math Forum

 January 5th, 2010, 10:38 AM #1 Newbie   Joined: Nov 2009 Posts: 2 Thanks: 0 grouping x^3-x^2+x-1 x^3-x^2+x-1 = x^2(x-1)+(x-1) = (x-1)(x^2+1) My question is, that is there any logic behind it? I do understand this: x^3-x^2+x-1 = x^2(x-1)+(x-1) But can you please explain that: x^2(x-1)+(x-1) = (x-1)(x^2+1) is it a formula or is there a logic behind it, that I can't see?
 January 5th, 2010, 10:44 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: grouping x^3-x^2+x-1 In general, ac + bc = (a+b)c, or c(a+b) Now for your example let a = x², b = 1, and c = (x-1) ac + bc = x²(x-1)+1(x-1) = (x-1)(x²+1) = c(a+b) Can you see it?
 January 5th, 2010, 10:45 AM #3 Senior Member   Joined: Nov 2008 Posts: 265 Thanks: 0 Re: grouping x^3-x^2+x-1 no problem you're correct: x^2(x-1) + (x-1) since you have a common (x-1) in the expression on both sides of the addition symbol, you can factor out (x-1) to get (x-1)(x^2 + 1) does that make sense?
 January 5th, 2010, 10:58 AM #4 Newbie   Joined: Nov 2009 Posts: 2 Thanks: 0 Re: grouping x^3-x^2+x-1 Oh yeah, now I see it. Thank you so much!

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