Question

" find a polynomial f (x) that satisfies the equation xf (x) + 71f (x) = x^2."

Answer 1

`x f(x) + 71 f(x) = x^2`


`f(x)(x + 71) = x^2`


`f(x) = (x^2)/(x+71)`

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.