Determine all polynomials
for all .
When the RHS = 0 so the LHS must be 0 as well; thus
Substituting then gives RHS = 0 again, so LHS must be 0
Continuing this way, we get Hence must have these five roots and so we have
where is some polynomial.
Thus the polynomial must satisfy for all and so must be a constant function. Hence
where is a real constant.