Answer Key 6.7

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1. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{20x^4}{4x^3}&+&\dfrac{x^3}{4x^3}&+&\dfrac{2x^2}{4x^3} \\ \\
   5x&+&\dfrac{1}{4}&+&\dfrac{1}{2x}
   \end{array}\)
2. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{5x^4}{9x}&+&\dfrac{45x^3}{9x}&+&\dfrac{4x^2}{9x} \\ \\
   \dfrac{5}{9}x^3&+&5x^2&+&\dfrac{4}{9}x
   \end{array}\)
3. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{20n^4}{10n}&+&\dfrac{n^3}{10n}&+&\dfrac{40n^2}{10n} \\ \\
   2n^3&+&\dfrac{n^2}{10}&+&4n
   \end{array}\)
4. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{3k^3}{8k}&+&\dfrac{4k^2}{8k}&+&\dfrac{2k}{8k} \\ \\
   \dfrac{3}{8}k^2&+&\dfrac{k}{2}&+&\dfrac{1}{4}
   \end{array}\)
5. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{12x^4}{6x}&+&\dfrac{24x^3}{6x}&+&\dfrac{3x^2}{6x} \\ \\
   2x^3&+&4x^2&+&\dfrac{x}{2}
   \end{array}\)
6. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{5p^4}{4p}&+&\dfrac{16p^3}{4p}&+&\dfrac{16p^2}{4p} \\ \\
   \dfrac{5}{4}p^3&+&4p^2&+&4p
   \end{array}\)
7. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{10n^4}{10n^2}&+&\dfrac{50n^3}{10n^2}&+&\dfrac{2n^2}{10n^2} \\ \\
   n^2&+&5n&+&\dfrac{1}{5}
   \end{array}\)
8. \(\begin{array}{ccccc}
   \\ \\ \\
   \dfrac{3m^4}{9m^2}&+&\dfrac{18m^3}{9m^2}&+&\dfrac{27m^2}{9m^2} \\ \\
   \dfrac{m^2}{3}&+&2m&+&3
   \end{array}\)
9. \(\polylongdiv{45x^2 + 56x + 16}{9x + 4}\)
10. \(\polylongdiv{6x^2+16x+16}{6x-2}\hspace{0.5in} \text{ or } x+3+\dfrac{22}{6x-2}\)
11. \(\polylongdiv{10x^2-32x+6}{10x-2}\)
12. \(\polylongdiv{x^2+7x+12}{x+4}\)
13. \(\polylongdiv{4x^2-33x+35}{4x-5}\)
14. \(\polylongdiv{4x^2-23x-35}{4x+5}\)
15. \(\polylongdiv{x^3+15x^2+49x-49}{x+7}\)
16. \(\polylongdiv{6x^3-12x^2-43x-20}{x-4}\)
17. \(\polylongdiv{x^3-6x-40}{x+4} \hspace{0.5in} \text{ or } x^2-4x+10-\dfrac{80}{x+4}\)
18. \(\polylongdiv{x^3-16x^2+512}{x-8}\)
19. \(\polylongdiv{x^3-x^2-8x-16}{x-4}\)
20. \(\polylongdiv{2x^3+6x^2+4x+12}{2x+6}\)
21. \(\polylongdiv{12x^3+12x^2-15x-9}{2x+3}\)
22. \(\polylongdiv{6x+18-21x^2+4x^3}{4x+3}\)