Polynomials decomposition into irreduceables

Question

I've been trying to find the composition to irreduceables of the following polynomials with no much success: X^2 +1 over the field F7 and X^2-2 over the field F5

Is there any method/algorithms I could use in order to solve this problem ? Can it be done using euclides algorithm and finding GCD ?

Thanks in advance !

Answer 1

Hint: your polynomials have degrees 2. So, if any of them has a proper divisor, then this divisor has degree 1.