Hi!

I need to prove that unique factorization works for polynomials. I think it might have something to do with the power of the polynomial and the number of roots...the hint in the problem suggested using the Euclidean Algorithm.

Thanks!

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- Jul 1st 2010, 10:23 AMsquelchy451Proving unique factorization for polynomials
Hi!

I need to prove that unique factorization works for polynomials. I think it might have something to do with the power of the polynomial and the number of roots...the hint in the problem suggested using the Euclidean Algorithm.

Thanks! - Jul 1st 2010, 01:02 PMTKHunny
Start by stating the theorem.

- Jul 1st 2010, 02:53 PMsquelchy451
you mean state the euclidean algorithm? It's a way of finding the GCD

If you have a and b, the process goes

a = (q1)b + (r1)

b = (q2)(r1) + (r2)

r1 = (q3)(r2) + r3

and keeps going on until the remainder becomes zero - Jul 1st 2010, 05:35 PMchiph588@
In general a ring $\displaystyle R $ is a $\displaystyle \text{UFD}\iff R[x] $ is a $\displaystyle \text{UFD} $.

- Jul 1st 2010, 05:50 PMsquelchy451
The number theory textbook i'm using says nothing about rings...ring R = UFD?

- Jul 3rd 2010, 09:04 PMsquelchy451
bump bump bmup

- Jul 3rd 2010, 09:13 PMroninpro
There are two steps that you need to take. First, you need to show that you can factor every polynomial into a product of primes / irreducibles. Then, you need to show that the factorization is unique.

Can you see how to prove either part? - Jul 3rd 2010, 09:44 PMsquelchy451
@roninpro yea I think i get it..io'llt ry that out and see how it goes.