Question

Suppose the result of dividing one polynomial by another is `r^2-6r+9-1/(r-3)`, what two polynomials might have been divided?

Answer 1

See below.

Explanation:

Supposing two polynomials `p(r)` and `q(r)` such that

`(p(r))/(q(r))=r^2-6r+9-1/(r-3) = ((r-3)(r^2-6r+9)-1)/(r-3)=`
`=(r^3-9r^2+27r-28)/(r-3)`

Calling now `phi(r)` a common factor polynomial, `p(r)` and `q(r)`

can be assumed to be

`p(r) = phi(r)(r^3-9r^2+27r-28)` and

`q(r) = phi(r)(r-3)`