it is easy to find the HCF of polynomials using euclid's lemma. so if you want to find the HCF of x^3-2x+14 and x^2-2, just do the following operation =>
HCF(x^3-2x+14-x(x^2-2),x^2-2)
=HCF(14,x^2-2)
=HCF(14,14(x^2-2)+2*14)
=HCF(14,14x^2)
=14
actually it can be any of 1,2,7,14 because of the 2nd step. then you have to do trial and error.
