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It is obvious the GCD of those two is 1.

The thing that makes me post this question is that why when using Euclidean Algorithm the GCD seems to be $ \frac{5}{4}$ ?

I want furthermore to find the inverse of the polynomial and i know i can do that when the GCD = 1 by using Extended Euclidean Algorithm. Yet as i've said i have 5/4.

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    $\begingroup$ $5/4$ is a unit (invertible) in the ring of polynomials with inverse $4/5$. It is like if you find that $-1$ is the gcd between two (rational) integers. People don't count an invertible factor. $\endgroup$ – OR. Jun 18 '17 at 10:58
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    $\begingroup$ Divide your whole equation by $5/4$ and you get an equation with 1. $\endgroup$ – OR. Jun 18 '17 at 11:19
  • $\begingroup$ OH RIGHT!! Thank you very much !! $\endgroup$ – Eduard6421 Jun 18 '17 at 11:26
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    $\begingroup$ That's the reason why people don't count units as interesting factors, you can divide them out as you need. $\endgroup$ – OR. Jun 18 '17 at 11:29
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So what? The conclusion (assuming that the computations are correct) is that $\frac54$ is a GCD of your polynomials. This is the same thing as saying that they are relatively prime.

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  • $\begingroup$ The thing is that furthermore i want to find the inverse of the polynomial. If from Euclid i didn't get 1 i don't know how am i supposed to continue\ $\endgroup$ – Eduard6421 Jun 18 '17 at 11:16
  • $\begingroup$ @Eduard6421 What's the problem? Start with $\frac54$ and express it as $\alpha(x)p(x)+\beta(x)q(x)$, where $p(x)$ and $q(x)$ are your polynomials. Then $1=\frac45\alpha(x)p(x)+\frac45\beta(x)q(x)$. $\endgroup$ – José Carlos Santos Jun 18 '17 at 11:18
  • $\begingroup$ I don't know how did i let that slip, that s completely obvious.. Thank you a lot! $\endgroup$ – Eduard6421 Jun 18 '17 at 11:27

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