Given information:
We are given three sets and we need to determine which of them is not a vector subspace of the vector space of polynomials with real coefficients.

Vector Space of Polynomials with Real Coefficients:
Let's denote the vector space of polynomials with real coefficients as V. V consists of all polynomials of the form p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_i are real numbers and n is a non-negative integer. V is closed under addition and scalar multiplication, and it contains the zero vector (the zero polynomial).

Subspace Criteria:
To determine whether a set W is a vector subspace of V, we need to check if it satisfies three conditions:
1. W is non-empty.
2. W is closed under addition, meaning that if p(x), q(x) ∈ W, then p(x) + q(x) ∈ W.
3. W is closed under scalar multiplication, meaning that if p(x) ∈ W and c is a scalar, then cp(x) ∈ W.

Analysis of the Sets:
a) W consists of all polynomials divisible by x.
- Non-empty: Yes, as the zero polynomial is divisible by x.
- Closure under addition: If p(x) and q(x) are divisible by x, then their sum p(x) + q(x) is also divisible by x.
- Closure under scalar multiplication: If p(x) is divisible by x and c is a scalar, then cp(x) is also divisible by x.
Therefore, W satisfies all the conditions and is a vector subspace of V.

b) W = {p(x) ∈ V ; p(3) = 0}.
- Non-empty: Yes, as the zero polynomial satisfies p(3) = 0.
- Closure under addition: If p(x) and q(x) satisfy p(3) = 0 and q(3) = 0, then their sum p(x) + q(x) also satisfies (p + q)(3) = 0.
- Closure under scalar multiplication: If p(x) satisfies p(3) = 0 and c is a scalar, then cp(x) also satisfies (cp)(3) = 0.
Therefore, W satisfies all the conditions and is a vector subspace of V.

c) W = {p(x) ∈ V ; p(a) = p(1-a), a ∈ R}.
- Non-empty: Yes, as the zero polynomial satisfies p(a) = p(1-a) for all a ∈ R.
- Closure under addition: If p(x) and q(x) satisfy p(a) = p(1-a) and q(a) = q(1-a), then their sum p(x) + q(x) also satisfies (p + q)(a) = (p + q)(1-a).
- Closure under scalar multiplication: If p(x) satisfies p(a) = p(1-a) and c is a scalar, then cp(x) also satisfies (cp)(a) = (cp)(1-a).
Therefore, W satisfies all the conditions and is a vector subspace of V.

Conclusion:
All three sets, a), b), and c), are vector subspaces of the vector