Factor Theorem & Synthetic Division...2

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 12, 2021.

  1. nycmathguy

    nycmathguy

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    Section 2.3
    Question 58

    20210910_210522.jpg

    Since x = 2/3, (x - 2/3) is a factor of the given polynomial.

    Using synthetic division, I got the following resulting coefficients: 48, -48, 9 with remainder 0.
    This leads to 48x^2 - 48x + 9.

    Factoring 48x^2 - 48x + 9, I got the following three factors: 3(3x - 1)(4x - 3).

    The real solutions are: x = 1/4, x = 3/4.

    You say?
     
    nycmathguy, Sep 12, 2021
    #1
  2. nycmathguy

    MathLover1

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    48 x^3 - 80 x^2 + 41 x - 6 = ((48 x^2 - 48 x + 9))*(x - 2/3) + 0

    48 x^2 - 48 x + 9=3(4x - 3) (4x - 1)

    then

    48 x^3 - 80 x^2 + 41 x - 6 =3(4x - 3) (4x - 1) (x - 2/3)
     
    MathLover1, Sep 12, 2021
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    I factored incorrectly. I can now say that the real solutions are x = 2/3, x = 1/4, and x = 3/4.

    Screenshot_20210912-072216_Samsung Internet.jpg
     
    nycmathguy, Sep 12, 2021
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