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5.9: Dividing Polynomials

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    For problems 1-6 use long division to perform the indicated division.
    1. Divide

    \[\frac{7 x^2+4 x-9}{x-1} .\]

    2. Divide

    \[\frac{8 x^3-4 x+1}{x+6} .\]

    3. Divide

    \[\frac{x^4-2 x^2+7 x}{x-4} .\]

    4. Divide

    \[\frac{2 x^4-9 x^3+2 x+8}{x+3} .\]

    5. Divide

    \[\frac{8 x^4+x^3-3 x^2+1}{x^2-2} .\]

    6. Divide

    \[\frac{4 x^5-7 x^3+x^2-4 x+2}{2 x^2-3 x-6} .\]


    For problems 7-11 use synthetic division to perform the indicated division.
    7. Divide

    \[\frac{-x^3-8 x^2+x+10}{x+2} .\]

    8. Divide

    \[\frac{10 x^3-9 x}{x-10} .\]

    9. Divide

    \[\frac{3 x^4+5 x^3+x-2}{x+7} .\]

    10. Divide

    \[\frac{x^4+2 x^3-9 x+11}{x+3} .\]

    11. Divide

    \[\frac{5 x^4-4 x^3+3 x^2-2 x+1}{x-1} .\]

    12. Desmos Exploration Choose one of Problems 7-11. Enter the polynomial into Desmos and evaluate the function at the value associated with the divisor \(x-c\).

    • Record the value of \(f(c)\).
    • Compare this value to the remainder from your synthetic division.
    • What relationship do you notice between \(f(c)\) and the remainder?
       

     

    5.9: Dividing Polynomials is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.