Can someone walk me through simplifying polynomials?

example problem:

(x + 4x^4) + (x^4 - 2 + 8x)

You can only add x terms together only if they have the same exponent. For example you can add 2x^2 and x^2 but you cannot add x^2 and x^3.

In this particular problem, you can add 4x^4 and x^4, and x and 8x. So,

(x + 4x^4) + (x^4 - 2 + 8x)

= 5x^4 + 9x - 2