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!

Printable View

- July 1st 2010, 11:23 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! - July 1st 2010, 02:02 PMTKHunny
Start by stating the theorem.

- July 1st 2010, 03:53 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 - July 1st 2010, 06:35 PMchiph588@
In general a ring is a is a .

- July 1st 2010, 06:50 PMsquelchy451
The number theory textbook i'm using says nothing about rings...ring R = UFD?

- July 3rd 2010, 10:04 PMsquelchy451
bump bump bmup

- July 3rd 2010, 10:13 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? - July 3rd 2010, 10:44 PMsquelchy451
@roninpro yea I think i get it..io'llt ry that out and see how it goes.