If segments CA and GA are part of the same line and GC is the total length, then GC = GA - CA.
Given: Length of CA = 9x^2 + 5x - 11
Length of GA = 14x^2 - 12x + 2
So, to find the length of GC:
GC = GA - CA
GC = (14x^2 - 12x + 2) - (9x^2 + 5x - 11)
GC = 14x^2 - 12x + 2 - 9x^2 - 5x + 11
GC = (14x^2 - 9x^2) + (-12x - 5x) + (2 + 11)
GC = 5x^2 - 17x + 13
Therefore, the expression that represents the length of segment GC is 5x^2 - 17x + 13.