what is the degree of 'f'

I'm not sure how you are supposed to figure this out but

 

\(f(x) = x^4 - 2x^2 \\ \text{and is of degree 4}\)

 

See if you can can work out what I have done.

See how in the 4th lot of subtracions the answer is the same each time.

That means it is a polynomial of degree 4.

 

x	F(x)	(1)	(2)	(3)	(4)
-3	63
-2	8	8-63=-55
-1	-1	-1-8=-9	-9--55=46
0	0	0--1=1	1--9=10	10-46=-36
1	-1	-1-0=-1	-1-1=-2	-2-10=-12	-12--36=24
2	8	8--1=9	9--1=10	10--2=12	12--12=24
3	63	63-8=55	55-9=46	46-10=36	36-12=24