Complete the synthetic division problem below. what is the quotient in polynomial form?

The polynomial would be 2x+5.

We bring down the first number inside the box, 2, unchanged.

   
-1|  2   7   5
   
      2

Now we multiply that 2 by the number outside, -1:
   
-1|  2   7   5
          -2     
      2

Now we add the two numbers in the middle column:
   
-1|   2   7   5
           -2       
       2   5

Multiply the 5 we brought down by the -1:
   
-1|   2   7   5
           -2  -5 
       2   5   

Add the numbers in the last column:
   
 -1|   2   7   5
            -2  -5
        2   5   0

The 3 numbers under the box represent the coefficients of x² and x, as well as the constant.  When we finish, we no longer have an x², but start at the next level down, which would be x.  2 would be the coefficient of x and 5 would be the constant, with 0 remainder.