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Linear Algebra

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Finite Dimension: Polynomial Subspace and Second Derivatives

LINALG-RIJXUD

Let $\mathcal{P}_n$ denote the set of all real-coefficient polynomials of degree at most $n$. This is a finite-dimensional vector space. Let $W = \{f(x) \in \mathcal{P}_{n}\mid f''(x) = 0\}$, which is a subspace of $\mathcal{P}_{n}$ for $n\ge 2$. What is $\dim(W)$?

A

$n+2$

B

$n+1$

C

$n$

D

$n-1$

E

$2$

F

$1$