your questions are mixed up
ok so if you had a ppolynomial that had a leading term of a and a constant of c, then
possilbe rational roots=+/-

therefor
+/-1/1 +/-3/1 +/-9/1
the bottom sign never changes therefor it was

therefor the leading term was 1 and the contatnt was 27
to find how many sole during 8th hour, just subsitue 8 for x
g(8)=8^3-8(8^2)+10(8)+27=80+27=107 tickets
you don't need synthetic division
constant is the one that doesn't change so that isi 27
constant is 27
tickets=107