How to write Horner's Algorithm in Mathematica?

The pseudocode we were given is:

Right now I have:

p[x_] := 6 (x + 3) + 9 (x + 3)^5 - 5 (x + 3)^8 - (x + 3)^11

For[k = 0, n - 1, k++, For[j = n - 1, k, n++, p[x]]]

integer n, k, j; real r; real array (a;)o:n for k = 0 to n - 1 do for j =n - 1 to k do a; t a; + raj+1 end for end for integer n, k, j; real r; real array (a;)o:n for k = 0 to n - 1 do for j =n - 1 to k do a; t a; + raj+1 end for end for