Exercise 1.  Factor each polynomial as a product of linear factors.  

1 (a).  .

Solution 1 (a).

See text and/or instructor's solution manual.

Answer.  .  

Solution.  Rewrite    as    and use the change of variable    to obtain  

                    .

Use the quadratic formula to obtain the roots of    

                      

Now solve for    and obtain  

                       and   .  

We could list these four roots as

                    ,   ,   ,   and  .

Using these four roots we write down the four linear factors of  

                      

We are done.   

Aside.  We can let Mathematica double check our work.

          The roots of the polynomial  ,  

          .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell