Solution:

Given f(z1,z2,z3)=z1²+z2²+z3²-z1z2-z2z3-z3z1=(z1-z2)(z2-z3)+(z2-z3)(z3-z1)+(z3-z1)

(z1-z2)

consider f(z2,z3,z1)=z2²+z3²+z1²-z2z3-z3z1-z1z2=(z2-z3)(z3-z1)+(z3-z1)(z1-z2)+(z1-z2)(z2-z3)

f(z3,z1,z2)=z3²+z1²+z2²-z3z1-z1z2-z2z3-=(z3-z1)(z1-z2)+(z1-z2)(z2-z3)+(z2-z3)(z3-z1)

here f(z1,z2,z3)=f(z2,z3,z1)=f(z3,z1,z2)

there for the factorization is cyclic symmetric.

This would help you better Algebra Homework Help.