2.3.H: Homework

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Perfect

    Divide Monomials

    In the following exercises, divide the monomials.

    1. \(20m^8n^4÷(30m^5n^9)\)

    Answer

    \(\dfrac{2m^3}{3n^5}\)

    2. \(\dfrac{45x^5y^9}{−60x^8y^6}\)

    Answer

    \(\dfrac{−3y^3}{4x^3}\)

    3. \(\dfrac{(−18p^4q^7)(−6p^3q^8)}{−36p^{12}q^{10}}\)

    Answer

    \(\dfrac{−3q^5}{p^5}\)

    4. \(\dfrac{(4u^2v^5)(15u^3v)}{(12u^3v)(u^4v)}\)

    Answer

    \(\dfrac{5v^4}{u^2}\)

    Divide a Polynomial by a Monomial

    In the following exercises, divide each polynomial by the monomial.

    5. \((8x^3+6x^2)÷2x\)

    Answer

    \(4x^2+3x\)

    6. \((48y^4−24y^3)÷(−8y^2)\)

    Answer

    \(−6y^2+3y\)

    7. \(\dfrac{72r^5s^2+132r^4s^3−96r^3s^5}{12r^2s^2}\)

    Answer

    \(6r^3+11r^2s−8rs^3\)

    8. \(20y^2+12y−1−4y\)

    Answer

    \(−5y−3+\dfrac{1}{4y}\)

    Divide Polynomials using Long Division

    In the following exercises, divide each polynomial by the binomial.

    9. \((a^2−2a−35)÷(a+5)\)

    Answer

    \(a−7\)

    10. \((4x^2−17x−15)÷(x−5)\)

    Answer

    \(4x+3\)

    11. \((p^2+11p+16)÷(p+8)\)

    Answer

    \(p+3−\dfrac{8}{p+8}\)

    12. \((2n^3−10n+28)÷(n+3)\)

    Answer

    \(\dfrac{2n^2−6n+8+4}{n+3}\)

    13. \((m^3+1000)÷(m+10)\)

    Answer

    \(m^2−10m+100\)

    14. \((125y^3−64)÷(5y−4)\)

    Answer

    \(25y^2+20x+16\)

    This page titled 2.3.H: Homework was last modified on Mon, 06 Jul 2026 03:20:45 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Kiersten Purves.