We’ll be working with the set P_n(\mathbb{R}), real polynomials of degree \leq n. Such polynomials can be expressed using n+1 scalar coefficients a_i as follows: [p(x)=a_0+a_1 x + a_2 x^2 + \cdots + a_n x^n]Vector spaceThe set P_n(\mathbb{R}), along with …