Basically, i am doing some cryptography, i need to show that a polynomial i have, which is not irreducibale, implies it is not primitive.(adsbygoogle = window.adsbygoogle || []).push({});

I am having trouble factorising these rather large polynomials.

I have checked to see whether the following polynomials are irreducible and found there factorisation with maple.

Could someone please teach me how you would do these by hand.

x^{5}+x+1=(x^{2}+x+1)(x^{3}-x^{2}+1)

Another example:

x^{5}+x^{4}+1=(x^{2}+x+1)(x^{3}-x+1)

an explanation of either would be gratefuly appreciated, thank you.

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# Irreducible polynomials

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