<PRE><B>Question 65343</B>
divide (a^3-5a^2+13a-14)/(a-2)
&lt;pre&gt;&lt;font size = 4&gt;&lt;b&gt;
Start out with this:
      
      &lt;u&gt;                   `&lt;/u&gt;
a - 2 )a³ - 5a² + 13a - 14
     
The &quot;a&quot; goes into the &quot;a²&quot; &quot;a&quot; times, so write &quot;a&quot; over the &quot;- 5a²&quot;

      &lt;u&gt;       a²          `&lt;/u&gt;      
a - 2 )a³ - 5a² + 13a - 14
       
Now multiply the a² by the -2 and get -2a² and write that below the 
&quot;- 5a²&quot;:

      &lt;u&gt;       a²          `&lt;/u&gt;            
a - 2 )a³ - 5a² + 13a - 14
          - 2a²
                       
                      
Now multiply the a² by the a, getting a³, so write that under the 
a³.                        
   
      &lt;u&gt;       a²          `&lt;/u&gt;                
a - 2 )a³ - 5a² + 13a - 14
       a² - 2a²
                        
Now draw a line and subtract (-5a²)-(-2a²) = -5a²+2a² = -3a². So write that under
the - 2a² termm, and bring down the next term, &quot; 13a&quot;
                                                     
      &lt;u&gt;       a²          `&lt;/u&gt; 
a - 2 )a³ - 5a² + 13a - 14   
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a

&quot;a&quot; goes into &quot;-3a²&quot;  &quot;-3a&quot; times. So we write &quot;- 3a&quot; above the &quot;+ 13a&quot; 
     
      &lt;u&gt;       a² -  3a    `&lt;/u&gt;
a - 2 )a³ - 5a² + 13a - 14
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a
           
Now multiply the -3a by both the a and the -2, getting -3a² + 6a.  Write
that at the bottom.
    
      &lt;u&gt;       a² -  3a    `&lt;/u&gt;
a - 2 )a³ - 5a² + 13a - 14
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a
           -3a² +  6a
                   
Draw a line and subtract: (+ 13a) - (+ 6a) = 13a - 6a = 7a. 
So write 7a under the 6a.  Bring down the last term &quot;-14&quot;
                   
      &lt;u&gt;       a² -  3a    `&lt;/u&gt; 
a - 2 )a³ - 5a² + 13a - 14
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a
          &lt;u&gt; -3a² +  6a&lt;/u&gt;
                   7a - 14
                    
&quot;a&quot; goes into &quot;7a&quot; &quot;7&quot; times, so write &quot;+ 7&quot; above the &quot;- 14&quot;
     
      &lt;u&gt;       a² -  3a +  7&lt;/u&gt;
a - 2 )a³ - 5a² + 13a - 14
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a
          &lt;u&gt; -3a² +  6a&lt;/u&gt;
                   7a - 14

Multiply the &quot;+ 7&quot; by both the &quot;a&quot; and the &quot;- 2&quot;, and get &quot;7a - 14&quot;, so
write this at the bottom 

      &lt;u&gt;       a² -  3a +  7&lt;/u&gt;
a - 2 )a³ - 5a² + 13a - 14
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a
         &lt;u&gt;  -3a² +  6a&lt;/u&gt;
                   7a - 14
                   &lt;u&gt;7a - 14&lt;/u&gt; 

Draw a line and subtract: (-14) - (-14) = -14 + 14 = 0
Write 0 at the bottom under the -14

      &lt;u&gt;       a² -  3a +  7&lt;/u&gt;
a - 2 )a³ - 5a² + 13a - 14
       &lt;u&gt;a² - 2a²&lt;/u&gt;
          - 3a² + 13a
          &lt;u&gt; -3a² +  6a&lt;/u&gt;
                   7a - 14
                   &lt;u&gt;7a - 14&lt;/u&gt;
                         0

Since the remainder is 0, the answer is a² - 3a + 7 that you
see at the top.

Edwin&lt;/pre&gt;     </PRE>