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

1 (c).  .

Solution 1 (c).

See text and/or instructor's solution manual.

Answer.  .

Solution.  

                    

Therefore    is a factor of  ,  and since the coefficients of    are all real

we know that    is also a factor of  .  Hence    is a factor of  .  

Now divide    by    and obtain

                    .

Therefore  .   

Next use the quadratic equation to find the roots of  .  


  


  

Hence,   .  

Combining this with the other factors    we obtain

                    .

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