How do I use synthetic division and the Remainder Theorem to find p(a)

Question

The numbers are p(x) = 5x^3 -12x^2 + 2x + 1 and a = 3

I know how to do synthetic division, but I am not sure what I am solving for or the steps I should take to get to the answer.

Answer 1

The process is the same as synthetic divisions, although it is called synthetic substitution because you a substituting 3 for x

3 | 5 -12 2 1

15 9 33

5 3 11 34

P(3) = 34