Determine if x - c is A Factor...1

Discussion in 'Algebra' started by nycmathguy, Jul 18, 2022.

  1. nycmathguy

    nycmathguy

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    College Algebra
    Chapter 1/Section 6

    Use synthetic division to determine if x - c is a factor of the given polynomial.

    IMG_20220718_114911.jpg
     
    nycmathguy, Jul 18, 2022
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  2. nycmathguy

    MathLover1

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    If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x - c) must be a factor.
     
    MathLover1, Jul 26, 2022
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  3. nycmathguy

    nycmathguy

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    The remainder here is not zero. This means my work is wrong.
     
    nycmathguy, Jul 26, 2022
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  4. nycmathguy

    MathLover1

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    your work is good
    -4 x^3 + 5 x^2 + 8 = (-4 x^2 + 17 x - 51)(x + 3) + 161

    so, the remainder of that division is 161, which means (x + 3) is not a factor
     
    MathLover1, Jul 26, 2022
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  5. nycmathguy

    nycmathguy

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    I totally get it. The remainder must be 0 for (x - c) to be a factor of f(x).
     
    nycmathguy, Jul 26, 2022
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