Example 3.  Use synthetic division (Horner's method) to find for the polynomial
        . 

Solution 3.

This example is for pedagogical purposes.  Our eventual goal is to use a vector for the coefficients, but for now we will enter them separately into each coefficient.  First we will check out the nested multiplication idea.  

Use the recursive formulas to compute the sequence  .  

Use the recursive formulas to compute the sequence  .  

We are done.

Aside.  We can check out the formulas

    
and
    

(c) John H. Mathews 2004