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

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Answer 1 · 2016-10-18T23:01:52

See below.

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

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

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