[tex]x f(x) + 71 f(x) = x^2[/tex]
[tex]f(x)(x + 71) = x^2[/tex]
[tex]f(x) = \dfrac{x^2}{x+71}[/tex]
We found f but it's not a polynomial, it's the ratio of two polynomials (given the slight misnomer of a rational function). There won't be any polynomial which makes this true for all x.
