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Math Help - 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
    Super Member

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    Lexington, MA (USA)
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    Hello, Hi888!

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


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

    \begin{array}{ccccccc}<br />
& & & & m^2 & +3m & -2 \\<br />
& & --- & --- & --- & --- & --- \\<br />
m^2-7 & ) & m^4 & +3m^3 & -9m^2 & -21m & +8 \\<br />
& & m^4 & & -7m^2 \\<br />
& & --- & --- & --- \\<br />
& & & 3m^3 & -2m^2 & -21m \\<br />
& & & 3m^3 & & -21m \\<br />
& & & --- & --- & --- \\<br />
& & & & -2m^2 & & +8 \\<br />
& & & & -2m^2 & +14 \\<br />
& & & & --- & --- & --- \end{array}

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . -6

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



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

    \begin{array}{ccccccc}<br />
& & & & d^2 & -4d & +1 \\<br />
& & -- & -- & -- & -- & -- \\<br />
d^2+2d+3 & ) & d^4 & -2d^3 & -4d^2 & -10d & +3 \\<br />
& & d^4 & +2d^3 & +3d^2 \\<br />
& & -- & -- & -- \\<br />
& & & -4d^3 & -7d^2 & -10d \\<br />
& & & -4d^3 & -8d^2 & -12d \\<br />
& & & -- & -- & -- \\<br />
& & & & d^2 & +2d & + 3 \\<br />
& & & & d^2 & +2d & + 3 \\<br />
& & & & -- & -- & -- \end{array}

    . . . . . . . . . . . . . . . . . . . . . . . . . . .0
    Answer: . d^2 - 4d + 1

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