It is entirely possible that, when looking for a given polynomial's roots, we might obtain a messy higher-order polynomial for S(x) which is further factorable over the "rationals" even before considering irrational or complex factorings.
====Limitations====It is entirely possible that, when looking for a given polynomial's roots, we might obtain a messy higher-order polynomial for S(x) which is further factorable over the "rationals" even before considering irrational or complex factorings.