Question

is the set p which is a subset of polynomials of degree less than or equal to 5 such that p(3)=p(5) a subspace of all polynomials of degree less than or equal to 5?

Answer 1

My understanding of the question is that p ={f|f(3)- f(5) = 0, deg(f) <6}.
\[0 \in p; \forall f_i \in p, \forall \alpha_i \in \mathbb{R}, \sum_{i}^{} \alpha_i f_i \in p .\]