Is the given polynomial irreducible:

(x^2)+x-2 in Z3, Z7?

Thanks. MK.

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- October 21st 2006, 06:01 PMMKLyonIrreducible Polynomial
Is the given polynomial irreducible:

(x^2)+x-2 in Z3, Z7?

Thanks. MK. - October 21st 2006, 08:23 PMThePerfectHacker
- October 21st 2006, 08:43 PMMKLyon
Why does it turn into -1 instead of -2?

Thanks for the earlier response. - October 21st 2006, 08:47 PMThePerfectHacker
- October 22nd 2006, 08:55 AMMKLyon
By this, I concluded that the equation was reducible in Z7[x] because 3 and 6 produced zeros. Can anyone confirm this?

- October 22nd 2006, 09:08 AMtopsquark
I believe MKLyon was talking about these -1s. He is correct that there is a typo. The lines should read:

which shows that the polynomial IS reducible in Z3[x].

(Okay, so the red coloring didn't work in the quote! You still get the idea.)

-Dan

PS: That x = 1 produces implies that x - 1 is a factor of the polynomial in Z3[x]. By doing the long division you can show that . Where is the x + 2 factor in the above list? Well, this would imply a root of x = -2 = 1 (mod 3), so really x = 1 again. This says that:

in Z3[x]. - October 22nd 2006, 09:12 AMtopsquark
- October 22nd 2006, 09:55 AMThePerfectHacker