Using Horner's Method I'm trying to evaluate a polynomial recursively using Horner's method.
It's rather simple when I have every value of $x$ (like: $x+x^2+x^3...$), but what if I'm missing some of those? Example: $-6+20x-10x^2+2x^4-7x^5+6x^7$.
I would also appreciate it if someone could explain the method in more detail, I've used the description listed here but would like some more explanation.

You can also carry it out in a synthetic division table.  Suppose you want to evaluate $f(x) = x^4 - 3x^2 + x - 5$ for $x = 3$. Set up a table like this


              1    0     -3    1     5
          3
             -------------------------
              1

Now multiply the number on the bottom and total as follows.


              1    0     -3    1     5
          3        3
             -------------------------
              1    3

Work your way across in this manner.


              1    0     -3    1     -5
          3        3      9   18    57
             -------------------------
              1    3      6   19    52

We have $f(3) = 52$.  Let's run a check
$$ f(3) = 81 -3*9 + 3 - 5 = 54 - 2 = 52.$$
$$ f(3) = 54 - 2 = 52.$$
This is a clean, tabular way to see Horner's method work.  
