Horner's Algorithm

You are given coefficients $(a_0,a_1,\dots ,a_n)$ of a polynomial

$p(x)=a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x+a_0,$

and a value $x=x_0$. Evaluate $p(x_0)$ using the minimum number of multiplications.

How many multiplications does the naive approach use, and how few can you get away with?