Question 672221
<pre>
Synthetic division can only be used when dividing by 

x+a or  x-a 

To divide  by x²-1 as in your problem,

{{{(2x^3+5x^2-4x-1)/(x^2-1)}}}

you can only use long division:

       <u>         2x+5</u>
x²+0x-1)2x³+5x²-4x-1
        <u>2x³+0x²-2x</u>
            5x²-2x-1
            <u>5x²+0x-5</u>
               -2x+4

Answer: 2x + 5 + {{{(-2x+4)/(x^2-1)}}}

However, you can do the long division synthetically
by writing only the coefficients, like this:

      <u>      2  5</u>
1 0 -1)2 5 -4 -1                
       <u>2 0 -2</u>
         5 -2 -1
         <u>5  0 -5</u>
           -2  4

and interpreting the quotient and remainder appropriately
by subtracting the largest exponent of the denominator from
the largest exponent in the numerator and writing this 
exponent of x by the coefficient of the first term in the
quotient. 

Edwin</pre>