Answer Key 6.7

  1. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{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}[/latex]
  2. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{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}[/latex]
  3. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{ccccc} \dfrac{20n^4}{10n}&+&\dfrac{n^3}{10n}&+&\dfrac{40n^2}{10n} \\ \\ 2n^3&+&\dfrac{n^2}{10}&+&4n \end{array}[/latex]
  4. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{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}[/latex]
  5. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{ccccc} \dfrac{12x^4}{6x}&+&\dfrac{24x^3}{6x}&+&\dfrac{3x^2}{6x} \\ \\ 2x^3&+&4x^2&+&\dfrac{x}{2} \end{array}[/latex]
  6. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{ccccc} \dfrac{5p^4}{4p}&+&\dfrac{16p^3}{4p}&+&\dfrac{16p^2}{4p} \\ \\ \dfrac{5}{4}p^3&+&4p^2&+&4p \end{array}[/latex]
  7. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{ccccc} \dfrac{10n^4}{10n^2}&+&\dfrac{50n^3}{10n^2}&+&\dfrac{2n^2}{10n^2} \\ \\ n^2&+&5n&+&\dfrac{1}{5} \end{array}[/latex]
  8. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{ccccc} \dfrac{3m^4}{9m^2}&+&\dfrac{18m^3}{9m^2}&+&\dfrac{27m^2}{9m^2} \\ \\ \dfrac{m^2}{3}&+&2m&+&3 \end{array}[/latex]
  9. [latex]\phantom{a}[/latex]
    5x+4 with no remainder
  10. [latex]\phantom{a}[/latex]
    x+3, remainder is 22, or x + 3 +22 over the difference of 6x minus 2
  11. [latex]\phantom{a}[/latex]
    x minus 3 with no remainder
  12. [latex]\phantom{a}[/latex]
    x+3 with no remainder
  13. [latex]\phantom{a}[/latex]
    x minus 7 with no remainder
  14. [latex]\phantom{a}[/latex]
    x minus 7 with no remainder
  15. [latex]\phantom{a}[/latex]
    x square + 8x minus 7 with no remainder
  16. [latex]\phantom{a}[/latex]
    6x square + 12x + 5 with no remainder
  17. [latex]\phantom{a}[/latex]
    x square minus 4x + 10, remainder is 80; or x square minus 4x +10 minus 80 over the sum of x+4
  18. [latex]\phantom{a}[/latex]
    x square minus 8x minus 64 with no remainder
  19. [latex]\phantom{a}[/latex]
    x square + 3x +4 with no remainder
  20. [latex]\phantom{a}[/latex]
    x square + 2 with no remainder
  21. [latex]\phantom{a}[/latex]
    6x square minus 3x minus 3 with no remainder
  22. [latex]\phantom{a}[/latex]
    x square minus 6x +6 with no remainder

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