Factoring

[beth56374]

I have been trying to figure out how to factor this equation: x^(2n-1)-2x^(n+1)+x
I have been lost on where to even begin... any help is much appreciated!!!

x^(2n-1)-2x^(n+1)+x

 

[Deleted member 4993]

I have been trying to figure out how to factor this equation: x^(2n-1)-2x^(n+1)+x
I have been lost on where to even begin... any help is much appreciated!!!

x^(2n-1)-2x^(n+1)+x

$\displaystyle x^{2n-1} - 2x^{n+1} + x$

Are you sure that the first power is (2n -1) and not (2n+1)

 

[beth56374]

Oh, yes it is 2n+1... sorry

 

[Deleted member 4993]

No wonder!!

x^(2n+1)-2x^(n+1)+x[/quote]

$\displaystyle x^{2n+1} - 2x^{n+1} + x$

$\displaystyle = x \cdot (x^{2n} - 2x^{n} + 1)$

substitute

u = x[sup:fk8w0pk0]2n[/sup:fk8w0pk0]

$\displaystyle x \cdot (x^{2n} - 2x^{n} + 1)$

$\displaystyle = x \cdot (u^2 - 2u + 1)$

Now continue...

 

[beth56374]

Thank you so much!!! Sorry about the confussion... wish I would've realized it a while ago :?