Factor Theorem & Synthetic Division...1

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 11, 2021.

  1. nycmathguy

    nycmathguy

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    Section 2.3
    Question 56

    Can you do 56 as a guide for me to try a few more on my own?

    20210910_210522.jpg
     
    nycmathguy, Sep 11, 2021
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  2. nycmathguy

    MathLover1

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    56.

    f(x)=x^3-52x-96
    x=-6
    =>(x+6) is a factor

    a.

    use synthetic division: if (x+1)=0=>x=-1

    -6| 1 0 -52 -96
    | -6 36 96
    |___________________
    ....1 -6 -16 0 =>resulting coefficients: 1,-6,-16,0

    the quotient is x^2-6x-16, and the remainder is 0

    factor it:
    x^2-6x-16
    x^2-8x+2x-16
    (x^2-8x)+(2x-16)
    x(x-8)+2(x-8)
    (x + 2) (x - 8)

    so,
    f(x)=x^3-52x-96
    f(x)=(x+6)(x + 2) (x - 8)

    real solutions:
    x=-6
    x=-2
    x=8
     
    MathLover1, Sep 11, 2021
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  3. nycmathguy

    nycmathguy

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    You said:

    "use synthetic division: if (x+1)=0=>x=-1"

    Where did (x + 1) come from?
     
    nycmathguy, Sep 11, 2021
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  4. nycmathguy

    MathLover1

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    if given root =x=-1, then factor is (x-root)=> in your case root =-1 then factor is (x-(-1))=>(x+1)
     
    MathLover1, Sep 12, 2021
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  5. nycmathguy

    nycmathguy

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    Sometimes I get confused with the easiest questions. Sad but true.
     
    nycmathguy, Sep 12, 2021
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