This is an excerpt from my math models textbook. It's about Lagrange Polynomials which is a technique that lets you fit a polynomial to a set of any number of unique points (x_1,y_1) ... (x_n,y_n) so long as all your x-values are different (otherwise it wouldn't be a function, and couldn't be a polynomial). The polynomial you'll calculate will be the unique, lowest degree polynomial that passes through all points.
If you have a series of (nx + m) terms multiplied together (where each n and m can be different), just count the number of times x comes up (let's call that z), and the order of the function will be x^z. For z = 3, that's cubic. None of the other terms matter for the expansion. If there's an x^3 and no higher powers of x, it will always be cubic and the coefficients of any of the terms are irrelevant.
If you're studying computer science, you can think of it like big O notation.
And for the other part, one trick for questions like that is to look at what happens when you substitute an equality they are talking about, specifically looking for terms that result in 0s or 1s and can be cancelled out of the equation. If you're not given actual values for any coefficients, there's not much else interesting you can do to a polynomial like that, other than maybe take the derivative or integrate.