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January 5th, 2010, 10:38 AM   #1
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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?
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January 5th, 2010, 10:44 AM   #2
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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 = x, b = 1, and c = (x-1)

ac + bc
= x(x-1)+1(x-1)
= (x-1)(x+1)
= c(a+b)

Can you see it?
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January 5th, 2010, 10:45 AM   #3
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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?
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January 5th, 2010, 10:58 AM   #4
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Re: grouping x^3-x^2+x-1

Oh yeah, now I see it.
Thank you so much!
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