Honors Algebra 2: Extra Practice Dividing Polynomials

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Divide. Simplify if possible. Include domain restrictions where necessary.

  1. \( \displaystyle \frac{a^{13}}{a^{10}} \)
    2. Solution

    \( a^{3}, a \ne 0 \)

  2. \( \displaystyle \frac{15x^{3}} {5x}\)
    3. Solution

    \( 3x^{2}, x \ne 0 \)

  3. \( \displaystyle \frac{35a^{2}} {7a^{2}}\)
    4. Solution

    \( 5a^{2}, a \ne 0 \)

  4. \( \displaystyle \frac{6a^{3} - 4a^{2} + 8a} {2a}\)
    5. Solution

    \( 3a^{2} - 2a + 4, a \ne 0 \)

  5. \( \displaystyle \frac{10n^{3} - 15n^{2} - 35n} {5n}\)
    6. Solution

    \( 2n^{2} - 3n - 7, n \ne 0 \)

  6. \( \displaystyle \frac{6a^{5} - 8a^{4} - 2a^{3} + 10a^{2} - 4a} {2a}\)
    7. Solution

    \( 3a^{4} - 4a^{3} - a^{2} + 5a - 2, a \ne 0 \)

  7. \( \displaystyle \frac{x^{5a} - x^{3a} + x^{a}}{ x^{a}} \)
    8. Solution

    \( x^{4n} - x^{2n} + 1, x \ne 0 \)

  8. \( \displaystyle \frac{x^{2} - 14x + 45} {x - 5}\)
    9. Solution

    \( x - 9, x \ne 5 \)

  9. \( \displaystyle \frac{20k^{2} + 27k - 14} {5k - 2}\)
    10. Solution

    \( 4k + 7, k \ne \displaystyle \frac{2}{5} \)