note that the right side of the equation is degree 4. since the two products are summed, that means both products on the left side would have to be 4th degree, also.

f(x) is multiplying a 4th degree poly ... so, wouldn't f(x) have to have degree 0 (i.e. , a constant) ?

so, what degree would g(x) have to be to form a product that is also 4th degree?