Linear algebra, polynomials and vectors.

Question

if $R_3[x]$ is all the poly. with a power less than 3 that all of its coefficients are from $\mathrm{R}$ (real)
is $4x^{-2}$ $\in$ to $R_3[x]$ ?
and all of the poly with negative powers, (because they are smaller than 3)

Answer 1

Degree of a Polynomial, unless otherwise stated starts from $0$. We generally don't consider negatives.