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Thread: Dividing Polynomials

  1. #1
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    Dividing Polynomials

    1. (m^4 + 3m^3 - 9m^2 - 21m +8) / (m^2 - 7)

    2. (-2d^3 - 4d^2 + d^4 - 10d + 3) / (d^2 + 3 + 2d)


    Please help me with this given items. I'll be using them as my reference guide because I cant understand it.

    Thanks in advance!
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  2. #2
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    Lexington, MA (USA)
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    Hello, Hi888!

    We're expected to know how to do long division . . .


    $\displaystyle 1.\;\;(m^4 + 3m^3 - 9m^2 - 21m +8) \div (m^2 - 7)$

    $\displaystyle \begin{array}{ccccccc}
    & & & & m^2 & +3m & -2 \\
    & & --- & --- & --- & --- & --- \\
    m^2-7 & ) & m^4 & +3m^3 & -9m^2 & -21m & +8 \\
    & & m^4 & & -7m^2 \\
    & & --- & --- & --- \\
    & & & 3m^3 & -2m^2 & -21m \\
    & & & 3m^3 & & -21m \\
    & & & --- & --- & --- \\
    & & & & -2m^2 & & +8 \\
    & & & & -2m^2 & +14 \\
    & & & & --- & --- & --- \end{array}$

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . $\displaystyle -6$

    Answer: .$\displaystyle m^2 + 3m - 2 - \frac{6}{m^2-7}$



    $\displaystyle 2.\;\;(-2d^3 - 4d^2 + d^4 - 10d + 3) \div (d^2 + 3 + 2d)$

    $\displaystyle \begin{array}{ccccccc}
    & & & & d^2 & -4d & +1 \\
    & & -- & -- & -- & -- & -- \\
    d^2+2d+3 & ) & d^4 & -2d^3 & -4d^2 & -10d & +3 \\
    & & d^4 & +2d^3 & +3d^2 \\
    & & -- & -- & -- \\
    & & & -4d^3 & -7d^2 & -10d \\
    & & & -4d^3 & -8d^2 & -12d \\
    & & & -- & -- & -- \\
    & & & & d^2 & +2d & + 3 \\
    & & & & d^2 & +2d & + 3 \\
    & & & & -- & -- & -- \end{array}$

    . . . . . . . . . . . . . . . . . . . . . . . . . . .0
    Answer: .$\displaystyle d^2 - 4d + 1$

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