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Linear Algebra

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Finite Dimension: Known-Root Polynomial Subspace

LINALG-K$VVNV

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 $c\in \mathbb{R}$ be an arbitrary, fixed scalar value. Let $W = \{f(x) \in \mathcal{P}_n\mid f(c) = 0\}$, which is a subspace of $\mathcal{P}_n$. What is $\dim(W)$?

A

$n+2$

B

$n+1$

C

$n$

D

$n-1$

E

$2$

F

$1$