Find a vector space complement to $\mathbb{R}(1 + x + x^2) + \mathbb{R}(x - x^2 - x^3)$ in $\mathbb{R}[x]\le_3$. (This is referring to the set of polynomials with degree less than or equal to 3.)
I am not sure I completely understand the process of finding vector space complements and it would be good to have one example of how to do it! Thanks for your help.