how do you factor this polynomial?

x^(2k+1) - y^(2k+1)

my teacher's answer is:

[x^2 (x^(2k-1) + y^(2k-1))] + [(y^2 - x^2)y^(2k-1)]

what is the reasoning involved to factor something as complicated as this?

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- Mar 3rd 2009, 04:08 PMoblixpscomplicated factoring problem
how do you factor this polynomial?

x^(2k+1) - y^(2k+1)

my teacher's answer is:

[x^2 (x^(2k-1) + y^(2k-1))] + [(y^2 - x^2)y^(2k-1)]

what is the reasoning involved to factor something as complicated as this? - Mar 3rd 2009, 05:20 PMAbu-Khalil

It's easily to see in this way when you are using induction to prove divisibility. - Mar 3rd 2009, 08:57 PMSoroban
Hello, oblixps!

Quote:

How do you factor this polynomial?

. .

my teacher's answer is: .

Wrong! . . . That is not factored!

The difference of two odd powers can always be factored.