Synthetic Division...A

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

  1. nycmathguy

    nycmathguy

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    College Algebra
    Section R.8

    137. Use synthetic division to find the quotient and remainder when x^3 - 4x^2 - 3x + 13 is divided by x - cuberoot{3}.
     
    nycmathguy, Apr 27, 2022
    #1
  2. nycmathguy

    MathLover1

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    • Take the constant term of the divisor with the opposite sign and write it to the left.
    • Write the coefficients of the dividend to the right.
    upload_2022-4-27_11-53-14.jpeg


    Step 1

    Write down the first coefficient without changes:

    upload_2022-4-27_11-53-59.jpeg

    Step 2

    Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

    Add the obtained result to the next coefficient of the dividend, and write down the sum.

    upload_2022-4-27_11-54-44.jpeg


    Step 3

    Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

    Add the obtained result to the next coefficient of the dividend, and write down the sum.


    upload_2022-4-27_11-55-35.jpeg


    Step 4

    Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

    Add the obtained result to the next coefficient of the dividend, and write down the sum.

    upload_2022-4-27_11-58-12.jpeg

    We have completed the table and have obtained the following resulting coefficients:

    upload_2022-4-27_11-59-10.jpeg

    All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

    Thus, the quotient is upload_2022-4-27_12-0-5.jpeg , and the remainder is upload_2022-4-27_12-1-0.jpeg


    Therefore, upload_2022-4-27_12-4-8.jpeg =

    upload_2022-4-27_12-3-39.jpeg
     
    MathLover1, Apr 27, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Wow! This is synthetic division at a different level.
     
    nycmathguy, Apr 27, 2022
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