Example 2.  Use the "Horner tableau" to find for the polynomial
        .  

Solution 2.

The fifth degree polynomial is

    .  

When n=5 the Horner tableau is

Substitute the coefficients    and     into the table and get

We are done.

Aside.  We can check out the quotient and remainder. The last step above gives us the coefficients of and  .

As before, in Example 1, we have:

        and    .
    
    
Then    
    
    
    

(c) John H. Mathews 2004