Why is $X^4-X^2+1$ reducible over $\Bbb F_5$? I have checked $X^4-X^2+1=0$ and got the solution that the polynom is never equal 0 so it should be irreducibel. 
However it is. 
My prof gave me that hint: 
$X^4-X^2+1=(X^2+aX+b)(X^2+cX+d)$
Unfortunately that did not really help me. How can I solve that equation and where does it come from ?

$$x^{4} - x^{2} + 1= x^{4} - 2 x^{2} + 1 + x^{2} = x^{4} - 2 x^{2} + 1 - 4 x^{2} =\\= (x^{2} - 1)^{2} - (2 x)^{2} = (x^{2} - 1 + 2 x) (x^{2} - 1 - 2 x)$$
