Classify -2x^4-x^3+8x^2+12 by degree

The answer is quartic. The degree of a polynomial is the highest power of any term. This information is useful to us because for larger values of positive and negative x, this term dominates the behaviour of the function.

Here the highest power is x^4, giving rise to order/degree 4. It would be just as correct to call it that, but the first few orders have specific names:

1 - linear
2 - quadratic
3 - cubic
4 - quartic
5 - quintic

I hope this helps you :)