<PRE><B>Question 169236</B>
&lt;pre&gt;&lt;font size = 4 color = &quot;indigo&quot;&gt;&lt;b&gt;
Use long division to find the quotient and remainder when 
{{{2x^5+4x^4-x^3-x^2+7}}} is divided by {{{2x^2-1}}}

We must fill in gaps in powers with terms with 0
coefficients. I also will put in 1-coefficients:

Write:
{{{2x^5+4x^4-x^3-x^2+7}}} as {{{2x^5+4x^4-1x^3-1x^2+0x+7}}}

and

{{{2x^2-1}}} as {{{2x^2+0x-1}}}


                         1x&lt;sup&gt;3&lt;/sup&gt; + 2x&lt;sup&gt;2&lt;/sup&gt; +  0x +  .5 
            ---------------------------------- 
2x2 + 0x - 1)2x&lt;sup&gt;5&lt;/sup&gt; + 4x&lt;sup&gt;4&lt;/sup&gt; - 1x&lt;sup&gt;3&lt;/sup&gt; - 1x&lt;sup&gt;2&lt;/sup&gt; +  0x +   7
             2x&lt;sup&gt;5&lt;/sup&gt; + 0x&lt;sup&gt;4&lt;/sup&gt; - 1x&lt;sup&gt;3&lt;/sup&gt;
             ---------------
                   4x&lt;sup&gt;4&lt;/sup&gt; + 0x&lt;sup&gt;3&lt;/sup&gt; - 1x&lt;sup&gt;2&lt;/sup&gt;
                   4x&lt;sup&gt;4&lt;/sup&gt; + 0x&lt;sup&gt;3&lt;/sup&gt; - 2x&lt;sup&gt;2&lt;/sup&gt;
                   ---------------
                         0x&lt;sup&gt;3&lt;/sup&gt; + 1x&lt;sup&gt;2&lt;/sup&gt; +  0x
                         0x&lt;sup&gt;3&lt;/sup&gt; + 0x&lt;sup&gt;2&lt;/sup&gt; +  0x
                         ---------------
                               1x&lt;sup&gt;2&lt;/sup&gt; +  0x +   7
                               1x&lt;sup&gt;2&lt;/sup&gt; +  0x -  .5
                               ---------------
                                           7.5


                            7.5
Answer:  x&lt;sup&gt;3&lt;/sup&gt; + 2x&lt;sup&gt;2&lt;/sup&gt; + .5 + ----------
                          2x² - 1
 
Edwin&lt;/pre&gt;
    </PRE>