Divide the following polynomials using synthetic division, then place the answer in the proper location on the grid. write answer in descending powers of x. (x3 - 2x2 - 1) ( x - 1)

To solve using synthetic division:

Draw an upside down division symbol (I did the best I can given the format). Place the constant of x - 1 (1) on the outside, and the coefficients of x³ - 2x² - 1 on the inside, like so:      

   | x³   x²   x¹   x⁰
1 | 1   -2    0   -1   
   |         
   |

Next, bring down the first coefficient.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1   
    |         
    | 
      1

Multiply the number on the outside of the symbol (1) by the coefficient you've just brought down (1). Place that number under the next coefficient to the right.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   
    | 
      1

Add the new number (1) to the coefficient above it (-2) and place that number directly underneath it.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   
    | 
      1   -1

Continue this process until you've run out of numbers to multiply.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   -1   -1
    | 
      1   -1   -1   -2

The resulting numbers are coefficients. The first three are part of the quotient, and the last one is part of the remainder. The remainder becomes the last coefficient (-2) over the divisor (x - 1).

(x³ - 2x² - 1) / (x - 1) = x² - x - 1 + -2/x - 1

1/125 probability for each student so, a 0.8 percent probably of winning per student.