Q: Is {polynomials of degree exactly 2} a vector space? What about P₂? Exactly 2: x² + (-x²) = 0 (degree 0!): NOT closed: not a vector space! P₂ (degree ≤ 2): closed ✓, all axioms: VECTOR SPACE! Dimension: 3 (basis {1, x, x²})! (Closure is key!)