Question 73065
You're on the right track by using synthetic division. But the value on in the box should be -1, since x+1=0  x=-1 is your zero

<pre>


          -1 | 2  1  -2  -1
               _____________
 
              2  <---------bring down the first term
                                     </pre>

<pre>


          -1 | 2  1  -2  -1
               __-2___________   Place the product of (-1) and 2 under the 1
 
              2  -1              Add the terms
                                     </pre>
<pre>


          -1 | 2  1  -2  -1
               __-2___1________   Place the product of (-1) and (-1) under the -2
 
              2  -1   -1           Add the terms
                                     </pre>

<pre>


          -1 | 2  1  -2  -1
               __-2___1___1_____   Place the product of (-1) and (-1) under the -2
 
              2  -1   -1   0        Add the terms
                                     </pre>
Since you get a remainder of 0 it shows that x+1 is a zero (which was already given, but we proved it). The qoutient coefficients 2  -1  -1 are then placed next to variables.
{{{2x^2-x-1}}}So this is your factor
If you multiplied {{{2x^2-x-1}}} by {{{x+1}}} you would get
{{{(2x^2-x-1)(x+1)=2x^3 +x^2 - 2x -1}}}So this is your factored form and your answer.
Hope this helps.