# Thread: Is the set of degree 2 or less polynomials with p(1)=p(2) a vector space?

1. ## Is the set of degree 2 or less polynomials with p(1)=p(2) a vector space?

Use the subspace theorem to decide whether the following set is a real vector space with the usual operations. The set V of all real polynomials p of degree at most 2 satisfying p(1) = p(2), i.e. polynomials with the same values at x = 1 and x = 2.

Subspace Thereom:
-The set is non-empty
- A1 is satisfied (closure under addition)
- S1 is satisfied (closure under scalar multiplication)

Really stuck on this!! Thanks in advance for any help

2. ## Re: Is the set of degree 2 or less polynomials with p(1)=p(2) a vector space?

Hey rmcal1.

Hint: Start off by stating what the vectors are and then show the axioms (zero vector, closure under scalar multiplication and addition).

In other words, what does a generic vector look like when you have p(1) = p(2)?