Suppose p∈P(R)p \in \mathcal P(\mathbf R)p∈P(R). Prove that there exists a polynomial q∈P(R)q \in \mathcal P(\mathbf R)q∈P(R) such that 5q′′+3q′=p5q'' + 3q' = p5q′′+3q′=p.
Define Dp=5p′′+3p′Dp = 5p'' + 3p'Dp=5p′′+3p′ and notice degDp=(degp)−1\deg Dp = (\deg p) - 1degDp=(degp)−1, then apply 3b/26