I am reviewing some problems from polynomial rings and hope that someone can tell me if I am on the right track..

PROBLEM: Let . If show that divides .

What I have done:

or

so

Thus is a factor of

Is this even close???? Thanks in advance

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- May 28th 2008, 09:52 PMginafaraHELP...Polynomial Rings Problem...
I am reviewing some problems from polynomial rings and hope that someone can tell me if I am on the right track..

PROBLEM: Let . If show that divides .

What I have done:

or

so

Thus is a factor of

Is this even close???? Thanks in advance - May 29th 2008, 12:33 AMMoo
- May 29th 2008, 02:39 AMkalagota
i think you are actually done but you missed some reasons.

note that or , that is

but the case cannot happen otherwise is a constant and that .

thus , that is is a constant function. but you have shown that and therefore . - May 29th 2008, 09:15 AMThePerfectHacker
If then .

Thus, since ,it follows so .

And thus .