From the graph we can observe the following characteristics:
a) The graph is rising towards the left and falling towards the right. Since the two ends of the graph are in opposite direction, the degree of the polynomial which is represented by the graph will be odd. In case of even degree, the both ends face the same direction.
b) The coefficient of the polynomial must be negative. Only in this case the graph will fall towards right and rise towards left. In case of a positive coefficient, the graph falls towards left and rise towards right.
So, the polynomial represented by above graph will have negative coefficient and odd degree, which is represented by option C.
So, the answer to this question is C