Question

Can synthetic division always be used instead of polynomial long division?

Answer 1

Yes

Explanation:

Because there is an expanded algorithm for synthetic division involving nonlinear and non-monic divisors

Answer 2

Yes, there is an expanded algorithm for synthetic division involving nonlinear and non-monic divisors (check out the w.i.k.i.pedia page on "synthetic division", under the "Expanded sythetic division" section).