Chapter 4 - Section 4.5 - Dividing Polynomials - 4.5 Exercises - Page 311: 6

$3m^4-2m^3-1$

Dividing the denominator to each of the terms of the numerator, the given expression, $ \dfrac{27m^4-18m^3-9}{9} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{27m^4}{9}-\dfrac{18m^3}{9}-\dfrac{9}{9} \\\\= 3m^4-2m^3-1 .\end{array}