As we know that the graph of a function log(x) is strictly increasing in the fourth quadrant and after x=1 it increases slowly but continues to increase throughout the first quadrant.
Now, it is given that the:
graph begins in the fourth quadrant and is increasing quickly.
graph crosses the point (1, 3) , the graph does not increase as fast after that.
The graph continues to increase slowly throughout the first quadrant.
The only way to do this one is by long division which I can't figure out how to show here. There are some great examples online if you google long division with polynomials.
The answer is 3x^2+3x+3 with a remainder of 5x+6 who's is usually shown as (5x+6)/2x^2 +2x+4 which was the divisor g(x).