Long Division

Discussion in 'Algebra' started by nycmathguy, Feb 27, 2022.

  1. nycmathguy

    nycmathguy

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    IMG_20220226_191433.jpg
     
    nycmathguy, Feb 27, 2022
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  2. nycmathguy

    MathLover1

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    \( f(x)=x^3-4x^2-5 \)

    find \(f(x) /(x-3)\)

    ________(\(x^2-x-3\)
    \((x-3)| x^3-4x^2+0*x-5 \)
    ......... \(x^3-3x^2\) .................subtract
    ................. \(-x^2+0*x\) ........................bring down +\(0*x\)
    .................\( -x^2+3x \)..subtract
    ......................... \(-3x\) .............bring down \( -5\)
    .........................\( -3x-5\)
    .........................\( -3x+9\) .......subtract
    ..............................\(-14 -\)>reminder

    => \( f(x) /(x-3)=x^2-x-3+(-14/(x-3))\)

    or,

    \(x^3 - 4 x^2 - 5 = (x^2 - x - 3)(x - 3) -14\)
     
    MathLover1, Feb 27, 2022
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  3. nycmathguy

    nycmathguy

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    Sorry but I could not follow your steps. Can you do this one on paper and then upload?
     
    nycmathguy, Feb 27, 2022
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  4. nycmathguy

    MathLover1

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    steps in one example:

    [​IMG]

    Step 1: Set up the long division.
    Step 2: Divide 1st term of dividend by first term of divisor to get first term of the quotient.
    Step 3: Take the term found in step 2 and multiply it times the divisor.
    Step 4: Subtract this from the line above.
    Step 5: Repeat until done.
    Step 6: Write out the answer.
    [​IMG]

    answer is:
    [​IMG]

    or [​IMG]
     
    MathLover1, Feb 27, 2022
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  5. nycmathguy

    nycmathguy

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    It now came back to me. Thanks.
     
    nycmathguy, Feb 27, 2022
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