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## Homework Statement

Let W = {p(t) ∈ P

_{4}(t): p(0)=0 }. Prove that W is a subspace of P

_{4}(t)

## Homework Equations

none

## The Attempt at a Solution

I know three things have to be true in order to be a subspace:

1. zero vector must exist as an element

2. if u and v are elements, u+v must be an element

3. if u is an element cu is an element

I'm a bit confused. I've done some searching on this forum + my textbook, and I haven't seen any questions in this particular format. Any help would be greatly appreciated.

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