"Determine if the given set is a subspace of Pn for an appropriate value of n. Justify your answers."

The first problem under these directions is -

"All polynomials of the formp(t) =at^2, whereais in R."

I know what the directions say...but I still don't really get exactly what it's asking. The back of the book says "Yes, by Theorem 1, because the set is Span {t^2}."

Theorem 1 - "If v1, ... , vp are in a vector space V, then Span {v1, ... , vp} is a subspace of V."

I don't get how this proves the above problem. To determine if something is a subspace, shouldn't I be given a vector? Or set of vectors? How does a polynomial with degree 2 fit into that theorem? Can anyone please explain what I should be trying to find in each problem like the one above or how to go about trying to find it? Any help is appreciated, thanks.