Question 1057682
To find the RATIONAL zeros, use the Rational Roots Theorem.  Make a list of all the possible roots to check, and check them using synthetic division, refactorizing each time, until you exhaust your list.


Roots {{{q/p}}} to check:
The pluses and minuses of q for 1,2,3,4,6,8,16,18,24;
p for pluses and minuses of 1, 2.


You can expect {{{-2}}} to be shown as a root, and {{{1.5=3/2}}} to be shown as a root.  You should find no other real nor rational roots; but unsure about any multiplicities ( I resorted to Google's graphing feature).