Linear Algebra Done Right · Problem 3D.20

Linear Maps — Sheldon Axler

Mathematics — Linear Algebra · invertible-linear-maps

Problem

Suppose

q \in \mathcal{P}(\mathbf{R})

. Prove that there exists a polynomial

p \in \mathcal{P}(\mathbf{R})

such that

q(x) = (x^2 + x)p''(x) + 2x p'(x) + p(3)

for all

x \in \mathbf{R}