SOLUTION: Carry out the following divisions and also write each in the form P(x)=D(x)Q(x)+R(x): {{{(x^2-x+1)/(x^2+x+1)}}} Thank you :)

P(x) = x² - x + 1 = original Polynomial
D(x) = x² + x + 1 = Divisor polynomial

So we divide the original Polynomial P(x) 
by the Divisor polynomial D(x) to find the
Quotient polynomial Q(x) and the Remainder
polynomial R(x). 

Here is the outline of the division you are
to do:

      Q(x)
D(x) )P(x) 
      ....
      R(x)    

So here is the division:

                      1
x² + x + 1)x² - x + 1
            x² + x + 1
                -2x + 0

So the quotient polynomial Q(x) is simply 1,
and the Remainder polynomial R(x) is -2x, so
putting it in the form P(x)=D(x)Q(x)+R(x),
we have:

     P(x)    =      D(x)  *  Q(x) + R(x)  
       |             |        |      | 
(x² - x + 1) = (x² + x + 1)(1) + (-2x)

Edwin