The Tau Toolbox, a mathematical library for integro-differential problems, has recently developed a 'polynomial' class. This class approximates functions using classical orthogonal polynomials, providing an efficient, user-friendly, and object-oriented framework. In this presentation, we elucidate the utility of this class in resolving linear ill-posed problems. It circumvents the need for explicit discretization by employing finite numerical linear algebra techniques. The Tikhonov regularization method and the truncated singular value expansion are incorporated. An error estimate is given for the solution of the Fredholm integral equation of the first kind, which is built from a low-rank approximation of the kernel followed by a numerical truncated singular value expansion. Numerical experiments illustrate the efficiency of this approach in computing accurate approximations for linear discrete ill-posed problems. This is achieved even when dealing with perturbed data functions, and requires no additional programming effort. A variety of test problems are used to assess the performance and reliability of the solvers. The end result is a numerical solution to a first-kind integral equation crafted using just two inputs provided by the user: the kernel and the right-hand side. The construction methodology closely mirrors the approach used in functional analysis.