Can someone explain this?(Taylor polynomials)

[NINHARDCOREFAN]

For function f(x)=1/(1+x^2), calculate Taylor polynomials for the 2nd and 4th degree about the point a=0.

The answer was:

P2 = 1-x^2;
P4 = 1-x^2+x.^4

for 2nd degree I got -2x/[(1+x^2)^2]
for 4th degree I got 12x/[(1+x^2)^4]

[Muzza]

But neither of your solutions are polynomials?

[NINHARDCOREFAN]

Why aren't they?

[Muzza]

http://mathworld.wolfram.com/Polynomial.html

Notice how every term in a polynomial must be of the form "some coefficient times an indeterminable x raised to some positive, integer power".