What is the quotient in polynomial form?

The correct answer is A) 2x+5.

Completing the synthetic division, first bring down the leading coefficient:
-1|  2   7   5
                   
      2

Now multiply this by the divisor, -1, and write it under the 7:
-1|  2   7   5
          -2     
      2

Now add the two values in the middle, 7 and -2:
-1|  2   7   5
          -2      
       2  5

Multiply the 5 by the -1:
-1|  2   7   5
          -2  -5
      2   5   

Add the 5 and -5:
-1|  2   7   5
          -2  -5
      2   5   0

This corresponds with an answer of 2x+5 and remainder of 0.