If g(x) is the fourth-degree function, then which of the following could be definition of g(x)?

When expanden, you are seeking the highest exponent of the x. 

Like in (A), you get an x² , a x and a constant. So the degree is 2. 

In (B), the (x+1)² generatrests a x². But the x in front makes x * x² = x^3 as the highest. This deg = 3. Expandet it all to see. Really, do it. 

Now do the same for all the others. What are their degrees?

Your answer will follow.

That's how its done.

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.

These are all factored so you can find all the roots easily.  Add up the roots, including when the multiplicity is more than 1 and that's the degree of polynomial it is.

The only one that is a fourth-degree polynomial is D.

D <–––––––