Given $P$, the vector space of all polynomials (over reals), I am supposed to come out with a hyperplane of $P$, and show that it is indeed a hyperplane.
Since a hyperplane is the same as a flat, I gave myself such example $p+M=\{p+q: q \text{ is in } M \}$ where $M$ is a subspace of dimension $n-1$, so $M$ is spanned by basis elements say $(1,x,x^2,...,x^n-2)$. I am now supposed to show that indeed it is a hyperplane. I am thinking of showing that the vectors $1-x^{n-1}, x-x^{n-1},\ldots, x^{n-2}-x^{n-1}$ are linearly independent?
Does this solve the question? Or you think I have to do something different?