Exercise 2.95: Define 
  
    P
    1
  
, 
  
    P
    2
  
, and

  
    P
    3
  
 to be the polynomials

  
    
      
        
          P
          1
        
        :
      
      
        
          x
          2
        
        −
        2
        x
        +
        1
        ,
      
    
    
      
        
          P
          2
        
        :
      
      
        11
        
          x
          2
        
        +
        7
        ,
      
    
    
      
        
          P
          3
        
        :
      
      
        13
        x
        +
        5.
      
    
  

Now define 
  
    Q
    1
  
 to be the product of 
  
    P
    1
  
 and 
  
    P
    2
  
, and 
  
    Q
    2
  
 to be
the product of 
  
    P
    1
  
 and 
  
    P
    3
  
, and use greatest-common-divisor
(Exercise 2.94) to compute the GCD of 
  
    Q
    1
  
 and 
  
    Q
    2
  
.
Note that the answer is not the same as 
  
    P
    1
  
.  This example introduces
noninteger operations into the computation, causing difficulties with the
GCD algorithm.127  To understand what is happening, try tracing
gcd-terms while computing the GCD or try performing the
division by hand.