Final answer:
The entire length of segment FG is twice the length of FN, since N is the midpoint. Therefore, FG is represented by the expression 4x^2 + 8x + 6.
Step-by-step explanation:
If point N is the midpoint of segment FG, then FN = NG. Since the length of FN is given as 2x2+4x+3, the length of NG will also be 2x2+4x+3. To represent the entire length of segment FG, we simply add the lengths of FN and NG together.
Thus, the expression that represents FG is:
FG = FN + NG
FG = (2x2+4x+3) + (2x2+4x+3)
Therefore, FG = 4x2+8x+6.