Example 1.  Use quadratic synthetic division to divide       by   .  

Solution 1.

First, construct the polynomial  .    

Second, given     construct the polynomials .    

Third, verify that  .

We are done.  

Aside.  We can have Mathematica compute the quotient and remainder using the built in procedures  PolynomialQuotient  and  PolynomialRemainder.   This is just for fun!

(c) John H. Mathews 2004